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THF liRSARY OF 
CG«GRES 3 , 

T wo G0P1E3 HEceiveo 

NOV, 25 1901 

Cor^OinHT ENTRY 

' Q - I ^ 0 I 

CLASS c*-XXa Ho.: 

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COPT J. / . 


Copyright, 1901 , 

By David A. Curtis. 

(yl LI Rights Reserved.} 



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Fllfcfc A RlDGC PAINTI** 00., 
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<jl Treatise comprising toe 

ANALYSIS of PRINCIPLED 

CALCULATION sf CHANCED 
CODIFICATION sf RULED 
STUDY Sf 5ITUAII0ND 
GlOSSAEYj/TOKER TERNS 


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T HERE is no reliable information to be obtained as to 
the origin of the game of Draw Poker. It has a 
slight general resemblance to several other games 
which have been played for an indefinite time, but none of 
these others has ever attained much vogue. 

It may be said without fear of contradiction, however, 
that it is an American game, though it is now played all 
over the civilized world. Its rules rest upon no original 
authority, since the inventor of the game is forgotten; and 
the game itself has been modified and improved from time 
• to time for at least two generations past, until now it is 
believed to have attained a practically perfect symmetry. 
The various changes made in the time mentioned have all 
been practical applications of the underlying principles of 
the game; and being adopted in the first place by some 
one club, or circle of players, have been gradually rec- 
ognized by other players and incorporated into their rules 
of play, until there is now practical unanimity among all 
poker players on all the essential points of the game. 

The literature of Draw Poker is already voluminous, 
but up to the present time no effort has been made to pre- 
sent the entire subject in a comprehensive form, embracing 
not only the fundamental principles of the game, but also 
the most approved methods of play as finally accepted by 
the best players throughout the country. 

This volume is offered as such a contribution to the 
devotees of the game. The author claims no authority be- 


IO 

yond a knowledge of the principles of the game and of the 
rules that are observed by the best players. When these 
rules conflict, even in minor particulars, that one has been 
selected which is most symmetrical and best conforms to 
the logic of the game, and it is confidently believed that 
the most scientific players will be the first to recognize the 
accuracy of the work. The author has originated nothing, 
but has collated all that has stood the test of actual play 
among experts. 


Description 



of the Game 


*3 


What Draw-Poker Is. 

T HE game is one in which a number of players each 
receive five cards out of a standard deck of fifty-two, 
obtaining them in regular order and in strict accord- 
ance with prescribed rules for dealing. After receiving and 
examining their cards they proceed to bet on what is called 
the value of the cards they hold, and the player who holds 
the most valuable ones, or who proffers a bet which no 
other player will cover, wins all the money which has been 
wagered on the deal. 

All rules in the game are founded on the principle that 
each player shall have exactly the same chance to hold valu- 
able cards, and exactly the same opportunity to bet on them 
that every other player has. Whatever advantage one has 
over another comes from his relative position at the table, 
and passes from one player to another in regular rotation, 
so that each one enjoys it in turn. 

The value, so-called, of the hands depends entirely on 
the rarity with which the particular combination of five, 
held by the player, occurs in the 2,598,960 possible combina- 
tions of five that can be found in a deck of fifty-two cards. 
It is governed, however, by the arbitrary values of the 
cards themselves, which are fixed as they are in whist, ex- 
cepting that the ace may be counted as either the highest 
or lowest of the thirteen cards in the suit, according to the 
desire of the player holding it. The values, therefore, of 
individual cards rank as follows: Ace, King, Queen, Jack, 
ten, nine, eight, seven, six, five, four, three, two, ace. 
Suits are of equal value. 


/ 


14 


This is all there is to draw-poker, but within this limit 
is an almost infinite variety. No combination, however, 
nor any situation in the game is possible, which is not gov- 
erned by the principles established and by the rules applied 
in draw-poker. 



t 


*5 


How the Game Is Played. 

D RAW-POKER is played by any number of persons 
from two to eight, or even nine. With less than 
four players, however, the game is likely to be unin- 
teresting, and with more than seven it is cumbersome, 
because of a delay which frequently occurs in the deal. 
Five or six players are best. 

There can be no legitimate partnerships in the game. 
Each one plays for himself. 

The sole object of the game is betting on the compara- 
tive merits of the cards held by the players. Each one bets 
on his own hand, as much or as little as he pleases, under 
the rules, and the winner in each deal takes all that has 
been wagered on the hands in that deal. 

For convenience in betting, chips are commonly used, 
though the game can be played without them, each player 
being provided with coin or bills. Chips, however, are re- 
garded as essential, and without them the game is likely to 
be greatly hindered. 

Before dealing the cards, each player buys as many 
chips as he desires from the banker, paying for them in 
cash. The banker stands ready at any time to redeem these 
chips at the same price at which he sold them. 

The players then cut for the deal, the low card, as in 
all games in which a full deck of fifty-two cards is used, 
giving the deal. The dealer then shuffles the cards. Any 
other player in the game may demand the privilege of 
shuffling, but the dealer has the last shuffle. He then pre- 


sents the pack to the player on his right, who is called the 
pone, to be cut. In cutting, at least five cards must remain 
in each packet, in accordance with the rule that not less than 
a complete hand shall be divided from the remainder of 
the deck. 

Before the deal, the player on the left of the dealer, 
who is called the age, places an ante, or blind, in the centre 
of the table, as the beginning of the pot that is to be played 
for. This is the only bet that is compulsory in the game, 
and the age, who is obliged to make it, enjoys, in compen- 
sation, a certain privilege which will be described presently. 

The amount of the blind is usually one or two white 
chips, “ two calling five," or requiring three more to fill, 
when it comes to the betting, as will be described presently. 
The blind, however, may be of any amount desired by the 
age, up to one-half of the limit agreed upon for the game. 
"The player on the left of the age has the privilege of 
straddling, or putting up twice the blind, providing he does 
it before the deal. If this is done, the next player to the 
left of the one who has straddled begins the betting after 
the deal, unless he has straddled the straddle, in which case 
the next player to his left begins. But no straddle can 
be more than one-half the limit. 

The dealer then gives one card at a time to each player 
at the table in regular succession, beginning with the age 
and continuing around toward the right, until each player, 
including himself, has five cards. The remainder of the 
pack he keeps in reserve. 

The next step is for each player to decide whether 
he desires to bet on his hand. The first to declare his inten- 
tion is the one on the left of the age or on the left of the 
last player to straddle if there has been a straddle. If he 
decides to risk his money, he must put twice the amount 
of the blind or last straddle in the pot. Should he decline 


i7 


to play, he must place his five cards, face down, in front of 
the age, as the beginning of the discard pile. If he bets, 
he must, as was said, put up twice as much as the age or 
last straddle put up before the deal, but he may, if he 
choose, make a further bet at the same time, of any amount 
he likes, up to the limit. This is in accordance with the 
general rule that any player, whose turn it is to bet, may 
increase the bet if he so desires at the same time that he 
puts up the money necessary to maintain his position in 
the game. 

After this player has signified his intention, either 
by throwing down his cards or by betting, the next player 
does the same. If he plays, he must put up an equal 
amount with the last player, and, if he chooses, he may 
raise, according to the same rule. One point must never 
be overlooked. It is essential to proper play that no player 
shall make a bet or throw down his cards until after the 
player next preceding him has done one or the other. 
Playing out of turn is a violation of rule. It is also unfair, 
and always makes confusion. 

All the players, in turn, signify their intention as di- 
rected until it comes to the age. He then does exactly as 
the others have done, with the exception that in putting 
up the same amount that the last player before him has 
bet, he is credited with the amount of his original blind. 
Providing no one has raised up to this time, it is enough 
for him to put up the same amount that he did at first, 
each of the others having simply doubled that amount. 
In such case, it is obvious that each player who stays in 
will have contributed equally to the pot. In case of a 
straddle the first round continues till each player has an 
equal amount in the pot. 

If any player, however, has raised in this betting be- 
fore the draw, it is also obvious that the age must put up, 


i8 


not only an amount equal to his blind, but an amount in 
addition that shall be equal to any and all raises that have 
been made. Should the age refuse to play, and throw his 
cards in the discard pile, he forfeits the amount of his 
blind, but is not compelled to put up any more. 

If there has been any raising each player continues to 
make good the full amount put up by the player next pre- 
ceding him, at the same time raising if he wishes to, till 
each one who stays has an equal amount in the pot with 
each other one who has stayed. The pot is then complete. 
Any player who refuses to make good to the amount of 
the preceding player's bet forfeits his claim to the pot and 
loses any money which he may have already contributed. 

Next comes the draw. Beginning with the age each 
player in turn tells the dealer how many cards he desires 
to draw, at the same time throwing into the discard pile 
as many cards as he calls for out of the hand originally 
dealt to him. He may call for as many or as few cards 
as he desires, up to five. In other words, he may keep any 
part of his original hand that he may want, or he may take 
an entire new hand. 

The dealer must satisfy each player in turn before deal- 
ing to the next, and it is the player’s business to see that 
he is satisfied at the time, before looking at the face of the 
cards he draws, and before allowing the dealer to go on 
to the next player. If he receives too many or too few 
cards, and does not speak till the dealer has begun serving 
the next player, his hand is foul and he has no remedy. If 
he has more than five cards he cannot play them, but loses 
all claim on the pot. If he has too few cards, he may, ac- 
cording to the usage in some clubs, play them as a complete 
hand, but he must announce the number which he actually 
holds before betting on the hand. In such a case he cannot 
hold a Straight, a Flush, or a Full. The latest usage, how- 


19 


ever, is to declare any hand foul which does not consist of 
five cards — no more, and no less — and this is logically 
the correct rule, since it is the player’s business to see that 
he gets five. 

Rules are given elsewhere, governing the accidents 
which sometimes result in the facing of cards in the deal 
or in the draw. 

In supplying the draw, the dealer serves himself last 
and must announce how many cards he draws, at the time 
of taking them. 

All the players being supplied, the final betting begins. 
The age, as compensation for his compulsory blind, has 
the last say, consequently the first to bet is the player on 
the left of the age. This holds good even if the age has 
passed out, as the privilege of the age never passes to an- 
other player. 

If the player to the left of the age has passed out, the 
one on his left bets first, no other player being allowed to 
bet or throw down his cards until his turn has come. In 
betting he places in the pot as many chips as he chooses, up 
to the limit, and if no one else puts in an equal amount 
afterward, he takes the pot without showing his cards, as 
there is no contest. 

The next player, if he contests, must put up as much as 
the first one has, and he may raise, if he chooses, any 
amount up to the limit. The other players follow in turn, 
each putting up the same amount as the preceding player, 
and at the same time raising if he desires to do so, till each 
player who remains in has the same amount in the pot with 
each other player who remains in, when the betting is closed. 

All that remains is the showdown. If only one player 
has remained in till the end, there is no showdown, but the 
last bettor takes the pot without telling what he holds. If, 
on the other hand, more than one player has stayed, each 


20 


one who is still in lays his cards face up on the table, and 
the one who has the best hand takes the pot. 

The deal then passes to the player who was the age; 
the one on his left becomes the age, and another pot is 
made and played for as before. This is the entire game of 
Draw Poker excepting when jack-pots are played. 


Ha.nds. 


A HAND, in Draw Poker, consists of the five cards 
held by a single player before or after the draw. Its 
value depends upon the combinations formed by the 
different cards. 

The highest hand in the game is the Royal Flush. This 
consists of Ace, King, Queen, Jack and ten of a single suit. 
The Royal Flush cannot be beaten, but can be tied by a 
Royal Flush of any other suit, and as there are four of 
these hands in the deck — one in each of the four suits — 
it follows, necessarily, that no one hand can present a 
mathematical certainty of winning. 

The next highest hand is the Straight Flush, which is 
not a Royal. That is, five cards of one suit in sequence, 
as the five, four, trey, deuce and ace of hearts, or the King, 
Queen, Jack, ten and nine of spades. The relative values 
of different Straight Flushes are determined by the de- 
nomination of the cards. One beginning with a Jack beats 
one that runs from a ten downward ; and one that contains 
an eight beats one that runs no higher than a seven. 

Next highest comes Fours. This is a hand containing 
four cards of the same denomination, as four Aces, four 
tens, or four deuces. As in all other hands the cards of 
higher denomination beat those of lower. Four eights 
beat four sevens ; four Aces beat four Kings, and so on. 

Next in value comes the Full, which is often called a 
Full Hand or a Full House. This consists of three cards 
of one denomination and two of another, as three Aces 
and two sevens, or three deuces and two tens. The triplets 


being the more valuable part of the hand, determine its 
value regardless of the denomination of the pair. Thus, 
three treys and a pair of fours, called a Trey Full on fours, 
beats three deuces and a pair of Aces, called a Deuce Full 
on Aces. 

The next hand in value is the Flush. This hand con- 
tains any five cards of one suit, unless they are in sequence, 
when the hand becomes a Straight Flush or a Royal Flush. 
Thus, the Ace, King, Queen, Jack and nine of diamonds 
is a Flush, and is beaten by any Full, but if the nine should 
be a ten the hand would be a Royal and could not be beaten. 
As between two Flushes the winning is decided by the 
highest card. Thus, the Ace, seven, five, four and deuce 
of one suit will beat the King, Queen, Jack, nine and seven 
of one suit. In case the leading cards of two Flushes tie, 
the next highest card in either hand decides, and, if these 
tie, the next highest decides, and so on. Thus, as between 
the King, nine, seven, five and deuce of diamonds, and the 
King, nine, seven, five and trey of clubs, the club hand wins. 

Next highest is the Straight. This is a hand contain- 
ing five cards in sequence, but of different suits, as the Ace 
of diamonds, King of hearts, and Queen, Jack and ten of 
spades; or the seven, six, five and four of clubs and the 
trey of hearts. The relative value of two Straights is de- 
termined by the denomination of the cards. One beginning 
with a Queen beats one beginning with a Jack, and so on, 
and two Straights headed by cards of the same denomina- 
tion will tie, regardless of the suits represented, since the 
four suits are of equal value. 

The hand ranking next below the Straight is Threes, 
Three of a Kind, or Triplets. This hand contains three 
cards of the same denomination, as three Aces and any 
two other cards not a pair, or three sevens and any other 
two cards not a pair. Threes cannot be tied, and rank ac- 


2 3 


cording to the denomination of the triplets, regardless of 
the denomination of the other two cards. 

Next comes Two Pairs, as two Aces, two fours and a 
Jack; or two sevens, two fives and a nine. As between two 
hands of this rank, the highest pair decides the value. 
Thus, sevens and deuces beat sixes and fives; Aces and 
treys beat Kings and Queens. In case the highest pairs in 
the two hands tie, the lower pair decides. Thus Kings and 
sevens beat Kings and sixes. In case both pairs tie, the 
denomination of the odd card decides, and in case the two 
hands are alike throughout in denomination, the hands tie. 

Next in rank comes a Pair. This hand contains two of 
one denomination, as two Kings, or two sevens, and three 
others of different denominations. Pairs outrank one an- 
other as single cards do. If there be a tie between the 
pairs, the highest card among the odd ones decides the 
value of the hand. If the highest odd cards tie, the next 
highest decides, and so on. 

The lowest hand contains none of these combinations 
and is not even distinguished by a name of its own, but is 
commonly designated by the name of the highest single 
card in it. Thus “ Ace high ” would mean a hand contain- 
ing an Ace and four other cards no two of which were a 
pair; “ Jack high ” would be a Jack and any four lower 
cards no two of which were a pair. Between such hands 
the highest card decides the value of the hand. Thus Ace 
high beats King high ; ten high beats nine high, etc. If 
the highest cards tie, the next highest decides. If these 
also tie, the next highest decides, and so on. 




Rules 


of the Game 


27 


FLules of Pla^y. 

T HE rules in Draw Poker relate mainly to : 

I. Preliminaries, including the blind and the straddle. 
II. The deal. 

TIL Betting before the draw. 

IV. The draw. 

V. Betting after the draw. 

VI. The showdown and settlement of bets. 

VII. Jack-pots. 

VIII. Errors. 


I. Preli min eyries. 

In taking seats at the table, if there is a choice of posi- 
tion, it should be decided by cutting the cards, the low card 
winning, and Ace being always low in the cut. 

Cards and chips are necessary. The cards are a stand- 
ard whist deck of fifty-two. The chips are counters of 
different colors representing different values, as agreed 
upon. Usually the white chips are smallest in value, the 
reds next, and the blues next. Yellow chips are also used 
for larger amounts. In a small game the white may be 
one cent, the red five, and the blue ten. In a larger game 
the white might be five cents, the red twenty-five, the blue 
one dollar, and the yellow five dollars. When the game is 
still larger the white are usually one dollar, the red five, the 
blue twenty-five, and the yellow one hundred. There is no 
arbitrary value. The amount represented by the different 
chips is agreed upon at the beginning, and one person is 
chosen as banker for the game. He takes possession of all 


28 


the chips at hand and sells them at the price fixed, redeem- 
ing them at the same price whenever any player may de- 
mand redemption, and in any event redeeming all that are 
outstanding at the end of the game. 

One most important detail must be agreed upon before 
the play begins. The game is either a limit, a no-limit, or a 
table-stakes game, and the decision as to which it shall 

be must be made before any bets are made. If it is to be 

\ 

a limit game, the amount of the limit is fixed by agreement, 
and no player can make any single bet to exceed the amount 
required to come in, plus the limit. That is, if no one else 
has yet betted, he cannot bet more than the limit, but if 
he has to see some one's else bet, he may see it and raise 
to the amount of the limit, but no more. 

If the game has no limit, he may bet as much as he 
desires, but in that case, any other player who is unable to 
see the bet that is made, may call for a show for his money. 
To do this, he must put up all he has, at the same time 
declaring that he has no more. The total amount staked 
by the player who calls for a show for his money together 
with an equal amount for each other bettor must then be 
put together on the table. This constitutes the original pot, 
to which all the contributors have an equal claim, the best 
hand among them taking the pot when the showdown 
comes. If, however, the other players than the one calling 
for a show, desire to continue betting among themselves on 
the merits of their hands, they can do so, keeping their 
further bets separate from the original pot. At the show- 
down, if the man who has called for a show holds the best 
hand he takes the original pot only. The outside bets go 
to the player holding the next best hand. If, however, the 
one who called for a show is beaten, the best hand takes all 
the money. 

The table-stakes game is made by each player putting 


29 


in sight on the table in front of him as much money as 
he desires to play for. There is no limit rule excepting that 
no player can add to the amount in front of him while a 
hand is being played, and any player may at any time call 
for a show for all he has in front of him. If he loses what 
he has originally displayed as his stake, he must retire from 
the game, unless the other players consent to his producing 
another amount which he is willing to play for. In that 
case, he declares this further amount to be his stake, and 
reenters the game. He may also declare additional money 
in any time he chooses, by the consent of the other players, 
provided there is no play going on at the time. He may 
not, however, look at his cards and declare more money in 
after seeing them. 

The player on the left of the dealer has the advantage 
of the age, or the privilege of the last bet. This he pur- 
chases by putting a blind in the pot before the deal. The 
blind is the only compulsory bet in Draw Poker, and is made 
in order that there shall be no futile deal, as there might be 
if there were no money on the table to play for. The usual 
blind is one white chip, but it may be any amount up to 
one-half the limit fixed for the game. A very common 
practice is for the age to put up a blind of two white chips, 
saying “ Two calls five,” meaning that the next player, 
if he desires to bet, must put up five chips. 

This blind, or compulsory bet by the age, is all the 
betting that is requisite before the deal. The player next 
on the left of the age, however, has the privilege of strad- 
dling the blind if he chooses to do so. To straddle is to 
put into the pot before the deal the amount called for by 
the blind. If it be the ordinary blind of “ one calls two,” 
two chips constitute a straddle. If the blind be “ two calls 
five,” the straddle is five chips. The effect of the straddle 
is to make the next player put up double the amount of the 


3 ° 


straddle before drawing cards. No player can straddle after 
seeing any of his cards. 

If the player having the privilege elects to straddle, the 
next player to him may straddle his straddle, by putting up 
double the amount of the first straddle. The next player 
may straddle again in turn by doubling the amount put up 
by the last player, with the restriction that no blind or 
straddle can be put up which will make the bet called for 
after the deal larger than the limit agreed upon for the 
game. And no straddle can be made by any player out of 
his turn. If the player whose privilege it is does not 
straddle, the next player may not do so. 

The cards must now be shuffled thoroughly by the 
dealer. Any player at the table may demand the privilege 
of shuffling also, but the dealer should shuffle last. After 
the shuffle he offers the deck to the player on his right, 
the pone, who cuts them, or touches the top card to signify 
that he does not desire to cut. If he cuts, he must cut 
so that there are at least five cards in each division of the 
deck. 


II. The Deal. 

The dealer then serves the cards one at a time to each 
player in turn, including himself, beginning with the player 
on his left, and continuing to the right around the table 
till each player has five cards, the dealer taking the last. 

Any error in the deal must be corrected before the play- 
ers lift their cards from the table, and before the deal has 
been completed. If it cannot be rectified without confusion, 
and without altering the sequence of the cards as they 
should fall to the several players, it is a misdeal. The 
cards must all be shuffled and cut again, and the same 
player deals. This is because the dealer’s error cannot be 
held to deprive the age of his privilege. A variation from 


3i 


this rule is made when jack-pots are played. In that case 
a misdeal calls for a jack-pot, and the deal passes to the 
next player. 

If it should happen that the error be not discovered until 
after the players have looked at their hands, the deal stands, 
but any player who has received too few or too many cards 
loses his chance to play in that deal. If he has already put 
money in the pot, he loses it. It is his own error that he 
has picked up too many or too few cards, and he is the 
only sufferer. 

An exception to this rule is frequently made when one 
player picks up a card belonging to another player together 
with his own five cards. By agreement between the two, 
the player with four cards may draw one from the other’s 
six, and the two hands may be played. 

In strict play, this exception should not be made in favor 
of the player who makes the error, since he has no right 
to pick up six cards. It is frequently allowed, however, as 
a strict adherence to the rule seems unduly harsh in such a 
case, unless the error is considered to have been made in- 
tentionally. It would seem that a fair remedy for this 
difficulty would be to declare a misdeal and deal the cards 
anew, but this would be obviously unfair to any player 
who might have received a good hand. The only proper 
course is to declare the two hands foul. The player who 
picks up a wrong number of cards must suffer for his 
own error. 

In case a card is faced by accident in the deal, the player 
to whom it was dealt must accept it, but if more than one 
card falling to any one player is so exposed, it is a mis- 
deal. The same dealer must deal again, because no player 
can be deprived, by the error of another player, of the priv- 
ilege of the age which falls to each one in rotation. 

Any error in the deal not described in the preceding 


3 2 


paragraphs, constitutes a misdeal. The same player must 
deal again, unless by agreement a misdeal calls for a jack- 
pot. Where the players are strongly in favor of jacks, and 
seek pretexts for making them, a misdeal is commonly reck- 
oned as such a pretext. 

Strictly speaking, it is an error for the dealer, having 
completed the fifth round, to start on the sixth, and this 
logically makes a misdeal, if even one card too many is 
separated from the deck. Players must agree among them- 
selves as to whether they will enforce this rule strictly. Any 
player, however, may demand its enforcement. 

III. Betting Before the Draw. 

The player on the left of the age, or, if there has been 
a straddle, the one on the left of the last straddler, is the 
first to announce whether he will play or not. If he does 
not care to bet on the cards he has, or on his chances in the 
draw, he says “ I pass,” and lays his cards, face down, in 
front of the age, where the discard pile should always be 
made. If he desires to play, he puts into the pot whatever 
amount is called for by the blind, or the last straddle. That 
amount is obligatory, but it is a fixed rule that whenever 
a player’s turn comes to bet, he may also raise as much as 
he chooses, up to the amount of the limit. Therefore, in 
addition to putting up the amount called for, he may also 
put up more if he desires, but not more than the amount 
called for plus the amount of the limit. He must, how- 
ever, put up the entire amount which he wishes to bet at 
one time. A player cannot make two bets on the same 
round. 

The next player then has his turn. If any player plays 
out of turn at any time, he is liable to loss, even if Rule 
VIII. be not enforced, for no one loses any privilege right- 
fully belonging to him by reason of another player’s error. 


33 


Therefore, if C comes in before B has played, B may still 
raise, as it was his right to do, and so make it cost C 
more than he expected to bet. If C should decline to see 
this raise he would forfeit what he had put into the pot by 
error, for any error in play is made at the expense of the 
player who makes it. It is a common usage, however, to 
allow him to withdraw the bet he made by error, if he 
refuses to play. 

Each player in turn makes his bet, or passes and lays 
down his hand. If he bets, he must put up as much as the 
player preceding him, and if he chooses to do so, may also 
raise. When it comes the turn of the age to play, however, 
he is credited with the amount of the blind he has already 
staked, and has only to put up an additional amount suffi- 
cient to equal what the last player has bet. If there has 
been no raise, this closes the betting before the draw. If, 
however, there was a straddle, or some one has raised, the 
play continues in the same order till each player has as much 
at stake as any other player has put up. If any player 
declines to see any raise, he forfeits whatever money he has 
already staked, and lays his cards in the discard pile. 

IV. The Draw. 

The pot being now made up, the players who have re- 
mained in the betting have the opportunity to draw, each 
one as many cards as he desires, to better his hand. If he 
chooses he may take five. When he calls for cards, how- 
ever, he must place in the discard pile out of the hand he 
already holds, as many cards as he calls for, and this he 
must do before receiving those he calls for. This must be 
done by each player in turn, no one being allowed to dis- 
card, or call for a draw before the player preceding him 
has been served. Disregard of this rule is unfair play, and 
though there is no penalty for it that can well be fixed, 


34 


good players will refuse to continue in a game with one 
who offends in this way. 

In serving the draw the dealer begins with the first 
player on his left, serving each one in turn with as many 
cards as he calls for, and satisfying each one in turn before 
serving the next. He must deal these cards one by one 
from the top of the remainder of the deck still in his pos- 
session, not including the discard pile. If there should be 
enough cards called for to exhaust the deck, he must not 
serve the bottom card, because that may have been seen 
by some of the players, but when he comes to that one he 
must place it in the discard pile. The discard must then 
be shuffled and cut and used in place of the original deck 
to complete the service of the draw. 

Should any player receive too many or too few cards 
in the draw, the rule is the same as in the original deal. 
He may demand that the error be rectified if he discovers 
it before the draw is completed. If not, his hand is foul. 
If the dealer has served the next player before his atten- 
tion is called to the error, he must complete his service to 
all the players and then deal the required card or cards 
from the deck. If any card, however, should be faced 
accidentally in the serving it goes in the discard, as the 
player to whom it falls cannot accept it. The dealer con- 
tinues as if no error had been made, until he has served 
all who desire to draw, and then serves the next card at 
the top of the deck in place of the one which was faced.* 

*An effort has recently been made by some players to change this rule, by 
C9mpelling the acceptance of a card faced in the draw, just as a card faced in the 
original deal must be accepted. This, however, is not good poker, as it gives the 
other players positive knowledge of what one player holds in his hand after the 
draw. 

Another variation that is played in some clubs is to make the dealer complete 
his service ;to the player whose card was faced, before serving the next who de- 
sires to draw cards. This is also objectionable as it affords a dexterous dealer the 
opportunity to deal dishonestly, and moreover it results in giving the other players 
different cards from those they should receive in the regular order. This last 
point may not be important, but any player has the right to insist upon it, and 
many do so. 


35 


V. Betting After the Draw, 

Betting after the draw is done in the same order as 
that before the draw. The player to the left of the age 
bets first. He puts in the pot as much as he desires to 
bet, up to the amount of the limit. If he is not willing 
to bet, he throws his hand into the discard pile. If the 
next player desires to bet, he puts up as much as the next 
preceding player has bet, and if he chooses, may raise any 
amount up to the limit. Each player who has remained in, 
does the same in turn, till each one has as much in the pot 
as any other one player has betted; then the pot is closed, 
and the showdown is in order. 

If, however, any player has made a raise or a bet which 
no other player is willing to cover, he takes the entire 
pot without showing his cards, and the next deal is in 
order. 

VI. The Showdown and Settlement. 

When the pot is closed, each player who has remained 
in till the close, lays his hand on the table face up, and 
the one showing the highest hand takes the pot, regardless 
of any words or any claim made which the cards do not 
justify. In case two or more players show equal hands, 
and no single hand beats them, those holding the highest 
hands divide the pot equally between them, the other play- 
ers taking nothing. If any player calls for a show for 
his pile, the procedure is according to Rule I. 

No bet in Draw Poker is made until the money is put 
into the pot. 

VII. Je^ck-pots. 

In playing for a jack-pot, the order of procedure is 
somewhat different from that prescribed by the preceding 
rules. In lieu of placing a blind on the table as the nucleus 
of a pot to be made up of the voluntary contributions of 


3 6 


those who desire to play after receiving cards, the pot is 
made up by each player chipping in an equal amount be- 
fore the deal. This, of course, does away with the blind 
and the straddle, and by making it compulsory for each 
player to contribute whether he has good cards or not, has 
a tendency to make the play faster and higher. The jack- 
pot is therefore favored by those who desire to push the 
action of the game, and is in disesteem among more con- 
servative players. 

It is, in consequence, often the case that a party will 
sit down to play jack-pots exclusively. The more common 
practice, however, is to play the ordinary game with oc- 
casional jack-pots interspersed among the others. The re- 
currence of the jack-pot is usually determined by the use 
of a buck, and by an agreement to play a round of jack- 
pots, or a whangdoodle, whenever Four of a Kind or a 
Straight Flush shall be shown in the game. By agreement, 
a jack-pot is played in some clubs whenever Three of a 
Kind or better is shown in play. No hand of this kind, 
however, is considered the occasion for a single jack-pot, 
or a whangdoodle, unless it is called and therefore shown 
by compulsion. 

The buck is any small object, such as a penknife, which 
is placed with the chips in the pot, at the beginning of 
the game. The winner of that pot takes it in, together 
with the chips, and holds it until it is his turn to deal. 
He then places it in the centre of the table and declares 
a jack-pot, at the same time putting up the amount for 
which the jack-pot is to be played. This amount is any 
sum, within the limit, which he may desire to make it. 
Each other player then puts up a like amount, and the pot 
is closed. 

When a whangdoodle is played, or the game is all 
jack-pots, it is a common custom, though not a matter of 


\ 


4 


37 


rule, for the dealer to put up the entire amount of the 
pot. As each player deals in turn, this makes the burden 
equal and avoids possible disputes. In such a case each 
dealer “ deals out his own pot/' or in other words, con- 
tinues to deal until the pot has been opened and played 
for. 

The pot being closed, the dealer serves five cards each 
to all the players, as in the ordinary game. The player 
on his left then declares himself first. If he has a pair 
of Jacks or better, he may bet. Otherwise he must pass, 
still retaining his cards, and the next player has a say. 
If he does not bet, the next, and then the next declares 
himself, till all have refused to bet or to “ open the pot,” 
as making the first bet is called. The pot is then sweet- 
ened by each player putting in a white chip, and the deal 
passes to the next player, unless it has been agreed that 
each one shall deal out his own pot; then the same player 
deals again. This last must always be done when there 
is a whangdoodle, or when the dealer has put up the en- 
tire pot, as explained. The pot is usually sweetened after 
each unsuccessful deal, but this may be omitted by agree- 
ment. 

No player is allowed to open the pot unless he has a 
pair of Jacks or better in his hand at the time of opening, 
which, as explained, is before the draw. If he opens by 
mistake without holding such a hand, he forfeits all claim 
to the pot, and to all that he has put up. If other play- 
ers, however, have joined in the play after such a false 
opening, they continue to play for the pot, exactly as if 
the opening had been legitimate. If the error is discovered 
before atvy play has been made, it is as if no such misplay 
had occurred, excepting that the player opening falsely for- 
feits his chance to play. It is a common practice in many 
clubs to require the player who has made this error to put 


33 


up the ante for the entire party in the next jack-pot, but 
the trouble with this rule is that there is no authority by 
which it can be enforced. The player can refuse to submit 
and there is no remedy excepting to manhandle him or to 
refuse to play longer with him. 

If a player has Jacks or better, he may open the pot 
or pass, as he chooses. If he opens, he puts in the pot as 
large a bet as he likes, up to the limit, at the same time 

N 

saying “ I open it for ” — as much as he puts up. The 
next player must then put up an equal amount, or pass, 
laying down his cards. He may bet without having Jacks 
if he desires to, and under the invariable rule that a player 
can always raise when it is his turn to play, he may raise 
if he desires, no matter what he holds, or does not hold. 

Each player in turn having bet, or laid down his cards, 
and all raises having been seen by all the players that re- 
main in, the pot is again closed, and the draw follows as 
in the ordinary game. After the draw, the player who first 
opened the pot makes any bet he chooses, up to the limit, 
and the others play in turn as in the ordinary game, the 
same rules governing the betting and the showdown. 

At the time of the showdown, the opener of the pot 
is compelled to show his hand, regardless of the betting, 
to prove the fact that he had the necessary openers. If 
he has not been called, however, he need show no more 
than enough of his hand to justify his having opened.* 

In regard to splitting openers, there has been much dis- 
cussion, and rules differ in different clubs. The most ap- 
proved play is not to allow the split. When it is allowed, 
the player must be careful to preserve the proof that he 
had openers before the draw. This he will best do by lay- 

* Rules differ on this point in different clubs. The one given above is, however, 
the best and most logical, since no player should be forced to show what he has 
betted on unless his bet is called, and if he show openers, he shows that he violated 
no rule in opening, which is all he can be called on to show. 


39 


in g his discard to one side and guarding it until the show- 
down. It has been argued against this, that by doing so 
he is liable to draw attention to the fact that he is split- 
ting, and so to betray his hand. This argument, however, 
is not good, for the risk of betraying his play is only a 
fair offset to the privilege of splitting, which he enjoys 
only by the indulgence of the other players. 

VIII. Errors. 

Any player playing out of his turn, whether in a jack- 
pot or in the ordinary game, forfeits his hand and all that 
he has put into the pot. This rule under some circumstances 
appears harsh, and it is not always enforced. As a matter 
of good play, and in justice to the other players, however, 
it should always be insisted upon. 

Any error in play (excepting those in the deal, as pro- 
vided for in Rule IV.) must be held to work to the dis- 
advantage of the player making it, since it is manifestly un- 
fair to make the others suffer in consequence. Thus, if 
a player puts chips into the pot by mistake he may not 
withdraw them except with the consent of all the other 
players. If his hand be dead for any reason, he forfeits 
any amount which he may have contributed to the pot and 
he cannot call for a new hand. 



Calculation 


of Chances 


< 


\ 


43 




Chances in Draw Poker. 

I N calculating the chances of any single bet made in the 
game of Draw Poker, the player has a number of dif- 
ferent things to take into account. The blind, as else- 
where explained, is a compulsory bet. So is the original 
stake which each player puts in as his contribution to a 
jack-pot, but every other bet in the game should be made 
only after all these various things are remembered and 
duly considered. 

Bets made are of two kinds, namely : those made in 
good faith on the chance of the player holding a better 
hand in the showdown than will be shown by any other 
player, and secondly, those made in the hope of convin- 
cing the other players that the bettor's hand is exception- 
ally strong, and that it is therefore useless for any other 
hand to be backed in opposition to it. Bets of the latter 
class are called bluffs, and the art of making them suc- 
cessfully is a part of what may be called the finesse of 
the game, in contradistinction to the mathematical science 
of it. 

The highest skill in Draw Poker undoubtedly consists 
in a combination of this finesse with the mathematical 
science; but inasmuch as the entire theory of the game is 
constructed on the basis of the mathematical chances, and 
inasmuch, also, as the art of finesse can never be thoroughly 
mastered by one who does not understand something, at 
least, of the percentages of chance, it is altogether advis- 
able to study the mathematics first. 

The things to be considered, then, in what may be called, 


44 


by way of distinction, a bonafide bet, may be classified as 
follows : 

1. The standing or value of the cards received in the 
deal (before the draw). 

2. The mathematical probability as to whether any other 
hand (before the draw) exceeds it in value. 

3. The mathematical chances of bettering one’s own 
hand in the draw. 

4. The odds to be obtained in the betting. 

5. The prospect of these odds being changed by other 
players coming in. 

6. The chance of a raise by some other player which will 
necessitate a choice between betting again and surrendering. 

7. The probabilities of other hands being bettered in 
the draw. 

8. The indications which may have appeared concerning 
the strength of the other players. 

In scanning this list it will immediately appear that the 
first four things specified may be determined more or less 
exactly by mathematics. To determine the first we must 
know what constitutes the value of a hand. 

, 1. The Relative Value of Hands. 

The lowest hand that can be held in poker is seven, five, 
four, trey and deuce of different suits. The highest hand is 
a Royal Flush. Between these two are so great a number 
of possible varieties that it would be an almost endless task 
to arrange a table in which each single combination of 
five cards would appear in a place between the next higher 
and the next lower combination of five. Even if such 
a table should be prepared, it would be too cumbersome for 
practical use, since there are 2,598,960 different combina- 
tions of five cards each, which are to be found in a standard 
deck of fifty-two cards. 


45 


Manifestly it would be a practical impossibility for any 
one to find a given hand, or combination of five, in this 
imaginary table, unless the table should be classified in 
some fashion, and he should understand the order of classi- 
fication. And since the work is too great to be done in 
detail, the classification and theoretical arrangement have 
been figured out according to the laws of permutation. 

Even to present these calculations in detail would neces- 
sitate a more voluminous work than this present book is 
intended to be. Therefore, only the results of the calcu- 
lation are to be given here. Enough may be said, however, 
of the method of classification to make the whole subject 
clear, and to enable any person with a taste for mathe- 
matical work to figure out for himself the accuracy of the 
values of the various hands as laid down by the rules of 
the game of Draw Poker. 

These values, it must be explained as a beginning, are 
fixed according to two rules. One is the arbitrary law ac- 
cording to which the thirteen cards of each suit are ranked, 
and the other is the number of times in which a combina- 
tion of a given sort will be found in the total of 2,598,960 
possible combinations in the deck. 

By analyzing the Royal Flush, which is accepted as the 
highest hand, we can see why it is so accepted. First, lay 
out the hand. It needs only a moment's thought to deter- 
mine that there are three other hands in the deck exactly 
similar to it, the different suits being all equal in value. 
There are, then, four Royal Flushes only in the deck (a 
fact which needs no demonstration), and the question is 
why this hand is held to be the highest. 

The first peculiarity of the hand which attracts atten- 
tion is that it is composed entirely of cards of one suit, 
so we call it a flush. Only a limited number out of all 
the possible hands can have this peculiarity, so we apply the 


46 


laws of permutation to learn how great or how small this 
number is. The calculation proves that there are 5,148 
flushes in the deck. 

We then look for some other peculiarity by which the 
Royal Flush is to be distinguished from other flushes, and 
the next thing that strikes us is that the five cards are in 
an uninterrupted sequence according to the arbitrary rule 
which establishes the comparative value of different cards 
of the same suit. The hand is therefore what we call a 
Straight. Having recourse again to the laws of permuta- 
tion we find that out of the 5,148 Flushes in the deck, there 
are 40 which are also Straights, and which rank therefore 
as Straight Flushes. 

Now, the Straight Flush has one characteristic which 
marks it as distinct from any other hand that is classified 
as a poker hand. No other card of the fifty-two in the deck 
can be substituted for any one of the five in the hand with- 
out altering some peculiarity of the hand, or altering its 
value. We have therefore discovered forty hands in the 
2,598,960 which are clearly different from all the others. 
They are therefore distinguished from all the others, and 
the fact that they are less likely to be held than any of 
the others, being less numerous than any other, is held to 
establish their value as higher than the others. 

It is perfectly clear that it would be possible to estab- 
lish any one given combination as the highest in the 2,598,- 
960 if everybody would agree to it. Thus the Jack of 
hearts, the seven of clubs, the five of spades, the three of 
hearts and the deuce of diamonds could be played as the 
most valuable hand in the deck by common consent. So 
could any other one hand. But a law of poker is that a 
hand to possess value must have some natural equality, re- 
semblance, or sequence in value, among the five cards com- 
posing it, to entitle it to distinction. The supposititious 


47 



hand mentioned has neither equality, resemblance, nor se- 
quence among its cards, and there is therefore no reason for 
its having any rank. 

In former times sequence was not counted as a part of 
poker. The resemblance of one card to another in the same 
hand, whether it was a resemblance of suit or equality in 
rank, was held to be the only characteristic that entitled the 
hand to recognition. There were therefore only seven va- 
rieties of hands known to the game, instead of the ten that 
are now recognized. When the sequence was recognized, 
the Straight was played as a hand. At first, it was reck- 
oned to be inferior in value to three of a kind. Mathe- 
matics, however, soon proved that it was a scarcer combina- 
tion among the 2,598,960 than Threes, and its rank was 
established accordingly. Then the Straight Flush was dis- 
covered, and as the Straight was already established, this 
also was promptly recognized. The mathematical test being 
applied, there was no difficulty in assigning it to its proper 
rank. 

It is not difficult to see at a glance how these forty 
Straight Flushes are differentiated in value, since the val- 
ues of individual cards are the same as those fixed in whist, 
with the sole difference that the Ace may be counted as 
the highest or the lowest, at the option of the player hold- 
ing it. These whist values being accepted, it is established 
as a rule in poker that when two hands are similar in other 
respects, the value of the highest card in either hand deter- 
mines the comparative rank of the hands, and in case the 
highest cards tie, the next highest determines. A Straight 
Flush, therefore, is ranked according to its highest card, 
which may be anything from a five spot to an Ace. When 
it is an Ace, the hand cannot be beaten and is therefore 
called Royal. It is one of the forty scarcest hands in the 
2,598,960 in the deck, and is the highest of these forty in 


4 ^ 



respect of its denomination, and therefore ranks as the high- 
est hand. 

Examination and analysis up to this point having shown 
us why the Royal Flush is properly ranked as the highest 
hand, our next step is to analyze the lowest hand in similar 
fashion, in order to see why it is the lowest. 

As stated, this lowest hand consists of any seven, five, 
four, trey and deuce in the pack, so that they be not all of 
the same suit. By spreading out five such cards and ex- 
amining them, the reason must appear, or else the prin- 
ciples of the game are erroneous. 

First, we perceive that the cards do not resemble one 
another in suit, and that no two of them are of the same 
value. It is true that there must be among the five at 
least two of one suit, for there are five cards and only four 
suits, but since there cannot be any hand without two cards 
of one suit in it, this resemblance in suit is not recognized 
as a characteristic unless it includes the whole five. If 
all are of the same suit, the characteristic is at once notice- 
able and the hand will be called a Flush, the value of which 
will be discussed presently. 

The five cards now under consideration, however, have 
no resemblance, as was said, and as we examine further, 
we see that they are not in sequence. It is true that there 
is a sequence of four, but, as in the case of* a Flush, the 
Straight is not recognized unless it includes the whole five. 
it is therefore a hand without any distinguishing character- 
istic, and for that reason is not entitled to any rank. 

Being without characteristics, and therefore without 
rank, the only value it can have must come from the denomi- 
nation of the five cards it contains. There are 1,302,540 
hands out of the 2,598,960 possible ones in the deck which, 
like this one, and including this one, have no rank for the 
reasons mentioned ; but this one is composed of the lowest 


49 


five cards that can be put together without including at 
least a pair. This will be seen after a little more study of 
the hand. If the Ace appears in a hand of this general 
character it counts, not as the lowest, but as the highest, 
so that the hand would be Ace-high. The deuce is abso- 
lutely the lowest, the trey next, the four next, and the five 
next lowest. These four must therefore appear in the low- 
est hand. The six is the next lowest, but if it be also in- 
cluded, the hand becomes a Straight. The next lowest must 
therefore be taken, and that is the seven, making the com- 
bination we are studying. 

The harmony of principle that exists in the game is 
further shown by the contrast between the frequency with 
which this lowest hand and the Royal Flush, which we 
have shown to be the highest, are to be found. There are 
only four Royal Flushes, but there are 1,024 hands in the 
deck, each of which is composed of a seven, five, four, 
trey and deuce. As four of these would be flushes, it re- 
mains that there are 1,020 variations of the lowest hand, 
and as the rarity of a hand is a prime consideration in deter- 
mining its value, the rules are all seen to be in harmony. 
It is true that there are 1,301,520 other hands besides this 
that are devoid of characteristics and are therefore classi- 
fied in the lowest rank, but each of them when examined 
will be found to contain some card of higher denomination 
than a seven, and will therefore be counted as of higher 
value. 

Our examination of these two hands has therefore 
shown us the various reasons why one hand is ranked 
above or below another, and it only remains to apply the 
laws of permutation to the entire number of 2,598,960 pos- 
sible combinations to see how many can be found of each 
of the various kinds that are entitled to a separate rank. 

As was said, there are 1,302,540 hands in which there 


/ 


5 ° 


is no resemblance of suit existing among the whole five 
cards ; no sequence of five ; and no two cards of the same 
denomination. These, being the most numerous, and being 
also colorless, are ranked as the lowest. A hand of this 
description is briefly called “ No Pair.” When two or more 
of this kind are compared, the one containing the highest 
card in denomination ranks highest. If the high cards tie, 
the next highest cards determine. If these also tie, the next 
highest, and so on. 

Next, we find that out of the entire number, there will 
be found 1,098,240 hands in which two cards of the same 
denomination or a single pair will appear. This hand is 
called “ One Pair ” and holds next rank to “No Pair,” 
being next to the most numerous. These pairs rank one 
another according to their whist values. In case of a tie 
in the pairs of two different hands of this rank, the high- 
est of the other three cards determines the rank of the hand ; 
and if there be a tie in the pairs and in the highest out- 
side card, the next highest determines, as before. 

Examining further, we find 123,552 hands in which 
there will be two pairs. As to its frequency of occurrence 
this hand comes third in the list, and for that reason, and 
also because it has more character, it outranks “ One Pair.” 
This hand is called “ Two Pairs,” but is frequently called 
after the higher pair of the two, as “ Aces Up,” meaning 
a pair of Aces and a lower pair, or “ Sevens Up,” meaning 
a pair of sevens and a lower pair. The comparative value 
of two such hands is determined by the whist value of 
the highest pair. Thus Jacks Up will beat Tens Up, even 
if it be Jacks and deuces against tens and nines. If the 
higher pairs tie, however, the value of the lower pair deter- 
mines. If these also tie, the odd card decides. 

The next most frequent hand will be found to contain 
three cards of the same denomination. There are 54,912 


5 1 


of these hands, and as the number diminishes, the character 
of the hand strengthens, three of one kind being more dis- 
tinctive in appearance than two pairs, as well as less fre- 
quent of occurrence. This hand is called “ Three of a 
Kind/’ or briefly “ Threes.” There can be no ties between 
Threes. 

Next in frequency will be found those hands in which 
there is an uninterrupted sequence in value from the highest 
to the lowest card in the hand, not all, however, being of 
the same suit. These are called “ Straights.” There are 
10,200 of them, and a tie between two of them remains a 
tie, there being no difference in the value of the suits. The 
Straight is the most frequent of what may be called the 
complete hands or those in which each card is necessary to 
make the whole of value. It is also the least distinctive 
in character, requiring, as it does, more than a single glance 
to determine its character. It is, therefore, for these two 
reasons accounted the lowest in value of the complete hands. 

Next comes the Flush, in which each of the five cards 
is of the same suit as the other four, but in which there 
is not a sequence in value. There are only 5,108 of these, 
and the Flush outranks the Straight, not only because it 
is less frequent, but because its distinguishing characteristic 
is more immediately apparent, being distinguishable at a 
glance, without examination. The comparative value of 
Flushes is determined by the denomination of the highest 
card. Thus, a Flush containing an Ace outranks one in 
which a King is the highest card, regardless of the value 
of the other four. In case the highest cards tie, the next 
highest determines, as before. 

Next highest in value, because next in rarity of occur- 
rence, comes the hand in which there are three cards of 
one denomination and two of another. It can hardly be said 
that its distinguishing characteristics are more apparent than 


52 


that of the Flush, but it is much scarcer than the Flush, as 
there are only 3,744 hands of this sort, and the rank is 
therefore entirely mathematical. This is called a “ Full,” 
a “ Full Hand,” or, sometimes, a “ Full House.” The com- 
parative rank of two Fulls is determined by the value of 
the Threes they contain regardless of the pairs, so there can 
be no ties. The Full is commonly called after the Threes 
it contains. Thus a Jack Full means one in which there 
are three Jacks and a pair. It will outrank a Ten Full, 
even though the pair in the latter hand may be higher than 
the pair in the former. 

Next highest, and the highest of all the incomplete 
hands, come those in which there are four cards of the same 
denomination. At the first thought it appears that there 
can be only thirteen of these hands since there are only 
thirteen denominations in the deck ; but a little consideration 
shows that each one of these thirteen may have any one 
of 48 other cards as the fifth card in the hand, so that there 
are 624 possibilities out of the 2,598,960 in which four of 
a kind may appear. This hand is called “ Four of a Kind,” 
or briefly “ Fours.” The comparative value of Fours is 
easily seen. There can be no ties. 

Next higher in rank comes the Straight Flush, which 
we have already examined, and highest of all the Royal 
Flush. 

II. Probable VaJue of Opposing H^nds. 

It is evident that if a number of hands are dealt from 
the deck, and only one of the number be examined, as is 
the case when a player receives his five cards from the 
dealer, the only way to estimate the comparative strengtli 
of the other hands will be by the law of averages. In Draw 
Poker there are indications to be noted, of the probable 
strength of opposing players, concerning which something , 
will be said later on. The first step of the player, however, 


53 


is to discover what he has himself received in the deal, and 
the second, to figure the standing of his own hand in com- 
parison with the mathematical chances of the others. His 
study of the indications referred to must follow these pre- 
liminary steps. 

Mathematically, then, he looks for the average hand, 
and this, he will find, is Ace-high. That is to say, there 
are about 200,000 possible hands in the deck which will be 
composed of an Ace and four other cards, none of which 
adds to the strength of the Ace. As we have seen, there 
are 2,598,960 possible hands in all, 1,296,420 of which are 
better than Ace-high. If he holds Ace-high, therefore, he 
knows that there are about the same number of possible 
hands lower than his, as there are of possible hands better 
than his. With one player against him he would be just 
as likely to win as to lose, betting on Ace-high. 

Evidently, if there are three players in the game, there 
are two even chances of his Ace-high being beaten. If 
there are seven in, the chances are multiplied accordingly. 

The next thing to remember is that two players hold- 
ing the same hand before the draw have the same chance 
of improving that hand in the draw. Therefore, the one 
holding the better hand before the draw stands the better 
chance of winning. While the draw may favor the lower 
hand, the even chance is that it will favor the higher one. 

As no good player will venture money repeatedly when 
the chances are against him, it is easily seen that it is an 
elementary principle of good play to establish what may 
be called a working average, and decline, ordinarily, to 
pay money for the privilege of drawing cards to any hand 
that falls below that average. A coup may sometimes be 
made by drawing to an almost hopeless hand if good cards 
happen to come in the draw, but justification for such play 
is only to be found when the player can get good odds in 


54 


the betting. If he gets five or six to one before the draw, 
he may risk his money on such a chance, even though he 
realizes that he has no show to win without striking luck in 
the draw. 

The working average is considered by most players to 
be a pair of eights or nines. With such a hand they con- 
sider, unless some other player has indicated his strength, 
that they have a fair chance of winning, and if they get 
ordinary odds in the betting, amounting to two or three 
to one or better, the play is a safe one. Conservative players 
* fix this average a little higher, and refuse to draw to less 
than a pair of tens or Jacks, but he who will not pay to 
draw to Jacks, unless he has a good reason to believe be- 
cause of some clear indication, that Jacks are worthless, is 
a timid player and likely to lose. 

III. The Chance of Bettering in the DtolW. 

The next thing to consider, in the order in which we 
have begun the study, is the chance the player has of im- 
proving his hand in the draw. As we have followed the 
game up to the point at which the draw occurs, a pot has 
been made up, to which each player has contributed an 
equal amount, relying partially on what cards he already 
holds, and partially on the chance he has of getting an im- 
proved hand in the draw. It is evident that unless he 
knows what the mathematical probability of improvement 
is, he cannot tell whether he has betted wisely or not be- 
fore the draw. 

Following are the chances of getting the various hands, 
the results only of calculation being given. It is easy to 
verify the statements by applying the laws of permutation, 
but to include all the figuring in this work would increase 
its size unduly. All that is here presented, therefore, is a 
summary to be used as a guide in actual play. 


55 


Royal Flush. — Drawing to four of a Royal Flush 
the chance is i in 47. There are 47 cards which the player 
has not seen, any one of which he may get, so that this is 
easily figured. 

Drawing to three of a Royal Flush the chance is 1 in 
1081. There are 47 cards unseen, and therefore 2 chances 
in 47 of getting one or the other of the two cards necessary. 
Supposing the first card received in the draw is one of the 
two, there remain 46 still unseen, and the chance is 1 in 46 
of getting the second. We therefore multiply 2/47 by 1/46 
to get the exact chance, and find it is 1 in 1081. 

As it is impossible in the game of Draw Poker to get 
odds of 1081 to 1 in the betting, no good poker player will 
venture money on this chance. It is true that some players 
do it occasionally as a “ flyer,” and it is on record that the 
play has been successful more than once, but it was purely 
accidental, and the player who tries such experiments is 
betting against all laws of chance. The writer has twice 
won money by filling a Straight Flush on a three-card 
draw, but the play was entirely unjustifiable. 

Following the same rule it is easy to see that the chance 
of filling a Royal Flush on a three-card draw is 1 in 16,215. 
On a four-card draw it is 1 in 178,365. 

Straight Flush. — If a single card be drawn to Ace, 
deuce, trey and four of one suit, the chance of filling the 
Straight Flush is the same as in drawing one to a Royal 
Flush. Only one card in the deck will fill it, and the chance 
is therefore 1 in 47. If the Straight Flush of four be any 
intermediate Straight, the same rule holds good. There is 
only one card which will serve. 

If, however, the Straight Flush of four be open at both 
ends, the chances are obviously 2 in 47. 

Drawing two cards to a three of a Straight Flush in- 
volves different conditions. If the three be, for instance, 


* 


5 6 


the Oueen, Jack and eight of clubs it is evident that the ten 
and nine of clubs are the only two cards in the deck that 
will fill a Straight Flush. But if the three cards held be 
the Queen, Jack and nine it is evident that either the ten 
and eight, or the King and ten, would fill. And if the 
three be the Queen, Jack and ten there is a still greater 
chance, for a Straight Flush may be made by drawing the 
Ace and King, the King and nine, or the nine and eight. 

No one of these chances, however, is large enough to 
consider. No player can be justified in betting on it or 
expecting it. If he draws to a three Flush, or Monkey 
Flush, at all, he is wasting the money he pays to draw, and 
does not deserve to win even on a Flush. 

Four of a Kind. — If the five cards held before the 

draw include four of a kind, the draw becomes merely an 

incident of play, designed to mislead the other players. It 

cannot better the hand, and the question whether to draw 

or not is to be considered solelv as a matter of finesse and 

* 

*not of mathematics. 

If three of a kind are held, and two cards are drawn, 
there are 2 chances in 47 of getting the fourth. If one card 
only is drawn, the chance is 1 in 47. 

If a pair is held, and three cards are drawn, the chances 
of making Fours is within an infinitesimal fraction of 1 in 
1160. If two cards are drawn to a pair, a kicker being held, 
the chance is 1 in 1081. 

If four cards are drawn, the chance of getting the other 
three of the same kind is approximately 1 in 4054. There 
is also 1 chance in 22,395 of drawing four of some other 
kind than the one held. 

Obviously, if a player's chance of winning a given pot 
depended solely on his holding Fours, he would not be 
justified in betting unless he held them pat, since he cannot 
get odds of 23 ]/ 2 to 1 in the betting. On anything less 


57 


than Fours already in his hand, therefore, the chance of 
filling Fours is only to be reckoned as one of his possibili- 
ties of winning. Combined with other possibilities they 
may justify his betting, but nothing less than Three of a 
Kind in hand presents a chance of making Fours in the 
draw sufficiently large to base a hope on. 

Full Hand. — Drawing one card to two pairs the 
chances of making a Full are 4 in 47. Drawing to Three 
of a Kind and a kicker, they are 3 in 47. 

Drawing two cards to Three of a Kind the chances of 
a Full are 72 in 1081, or almost exactly 1 in 15. 

Drawing two cards to a pair and a kicker the chances 
of a Full are 6 in 1081, or approximately 1 in 180. 

Drawing three cards to a pair the chances of a Full 
are 180 in 16,215, or almost exactly 1 in 90. 

Flush. — Drawing one card to a four Flush the 
chances are 9 in 47 of filling. There are nine cards of the 
suit among the 47 which remain unseen. 

Drawing two cards to a Monkey Flush the chances of 
filling are 90 in 2162, or almost exactly 1 in 24. 

Drawing three cards to two of the same suit the chances 
for a Flush are about 1 in 98. 

Straight. — Drawing one card to a four Straight the 
chances of filling are 8 in 47, if the Straight is open at 
both ends. If it be an intermediate, or one with an Ace 
at either end, that you are drawing to, the chances are 4 
in 47.* 

Drawing two cards to three of a Straight, if one of 
the three is an Ace, the chances of filling are 32 in 2162 

♦There is an apparent contradiction between the chances of filling a four 
Flush, and the chances of filling a four Straight. The four Flush is the easier to 
fill, yet the Flush is the more valuable hand, and this seems to be at variance with 
the principles of poker. A little consideration, however, will show that the four 
Straight is far more common than the four Flush. You do not hold the four Flush 
nearly so often as the four Straight, but if you hold it you have a better chance of 
filling it in the draw. 


% 


58 


or 2 in 134. If there be no Ace among the three, the 
chances of filling will vary according to the variety of 
ways in which the Straight may develop. For example, 
it is easier to fill a Straight by drawing to Queen, Jack 
and ten than it is by drawing to a King, Jack and ten. The 
first becomes a Straight if you draw an Ace and King, a 
King and nine, or a ten and nine, but to fill the latter you 
must get a Queen and either an Ace or a nine. In either 
case the chance is too small to justify a bet, and therefore 
need not be calculated. 

Three of a Kind. — Drawing three cards to a pair, 
the chances of making Three of a Kind are 6 in 47. * Draw- 
ing two cards to a pair and a kicker, the chances of Three 
of a Kind are 4 in 47. 

Two Pairs. — Drawing three cards to a pair, the 
chances of making two pairs are 16,212 in 97,290, or al- 
most exactly 1 in 6. Drawing two cards to a pair and a 
kicker the chances are 9726 in 97,290, or about 1 in 10. 

One Pair. — Drawing one card to four odd ones the 
chances of a pair are 12 in 47. Drawing two cards to three 
odd ones the chances are 18 in 47 of matching one of the 
three, plus the chance of the two that are drawn being a 
pair, which is about 1 in 15, making the total chance ap- 
proximately 2 in 5. Drawing three cards to two odd ones 
the chance of a pair is very nearly the same; and drawing 
four the chance is not far from even that a pair of some 
sort will be found in the hand after the draw. 

IV. The Betting Odds. 

In calculating the odds of any bet two things are cer- 
tain. In the first place the player puts up his money as 
against that which is already in the pot. No other money 
can be reckoned with any certainty, inasmuch as the other 
players may all refuse to bet after him, even though some 


59 


or all of them may have the right to do so. The actual 
odds obtained, therefore, are the money already in the pot, 
be it much or little, as against that which the player is 
putting in. 

But, in the second place, unless the player has the last 
say, being the age, or sitting next on the right of the 
last player who has raised, there is the contingency of a 
change in the situation to be remembered. Any player 
whose right it is to bet after the one who is now being con- 
sidered may raise him instead of seeing him. 

At this point many players err in thinking that the 
former odds are to be remembered and included in the new 
calculation that is necessary after being raised. This is not 
true. What a player has ventured already has nothing to 
do with the odds he gets on his new bet when he comes to 
bet again. And the wisdom of refusing to bet is in no wise 
affected by the fact of his having, or not having, previously 
contributed to the pot. 

To make this clear, suppose that there is $17 in the 
pot, of which the player has contributed $3. Since he 
put up his $3 some other player has raised $2, and 
if the first bettor still desires to play he must put up $2 
more. The obvious and perfectly natural thought is that 
as he has put up $3 already and is to put up $2 more he 
will be getting odds of 14 to 5. As a matter of fact, how- 
ever, the $3 which he put in originally no longer belongs 
to him but to the pot. For the purpose of calculating his 
further bet he must proceed on the assumption that his 
first bet is already lost. The odds he really gets in the bet 
now contemplated are 17 to 2. This will be manifest when 
it is remembered that his first bet will be absolutely lost if 
he decides not to put up the $2. 

Of course, in the event of his winning the pot his actual 
profit will consist of only the amounts that the other players 


6o 


have put up. He cannot reckon his own contributions as 
winnings. The point to be remembered, however, is that 
each bet is made at the actual odds as described, regardless 
of the amount that the player has already contributed. In 
other words, when it comes to a second or third bet the 
player is betting against the money that he himself has 
previously contributed. It is very important to keep this 
in mind. 

It is an elementary proposition that if a man shall con- 
tinue to make bets at given odds, on the happening of some 
event, when the chances of the occurrence are less than his 
own percentage in the pool, he will lose his money in the 
long run. If, therefore, in Draw Poker, he puts a greater 
proportion into a pot than is represented by the mathe- 
matical probability of his holding the winning hand, he is 
betting wildly. If he continues to do this, there is almost 
a certainty of his “ going broke/' It is conceivable that by 
a freak of luck he might win a great many foolish bets, 
just as he might possibly win a succession of capital prizes 
in a lottery, but no sane man would expect such a happening. 

To illustrate this, suppose two men to be playing poker. 
A has a four Flush before the draw, and B puts up a bet. 
It is evident that before cards can be drawn, A must have 
an equal amount with B in the pot, so that he can get no 
odds whatever in the betting. His only chance of better- 
ing his hand in the draw, or practically his only chance, 
since his four cards are all small, is in drawing a fifth of 
the same suit. It is tolerably certain that B has something 
better than a four Flush in his hand, else he would not have 
betted. If A bets, therefore, he is putting up even money 
on the chance of filling his flush. But, as we have already 
calculated, he has only 9 chances in 47 of filling. It is 
therefore just about as foolish for him to play as it would 
be for him to bet even money on throwing a given number 


out of the box with one die — a thing that no dicer would 
think of doing. 

Whenever a player, then, is called on to put chips into 
a pot, he should see how many are already in. This will 
tell him the odds in the betting. If he judges that his 
chance of holding the best hand is as good as his percentage 
in the pot, it is a good bet. If not, he is betting against odds. 

V. The Known and the Unknown. 

Up to this point we have considered those elements 
of chance involved in the betting which are determinable 
by pure mathematics. So far as these are concerned, the 
player who is quick in perception and has the mathematical 
mind will have little difficulty in determining as to the wis- 
dom or unwisdom of betting on the cards he holds. This, 
however, is only a small part of the science of the betting 
and has nothing to do with the finesse of the game. The 
other things to be considered can only be estimated — not 
calculated. 

It must be remembered that the player who ventures a 
stake in Draw Poker must not only take into consideration 
the cards he holds in his own hand, but those also which the 
other players hold. He has positive knowledge of the one, 
but no knowledge whatever of the other, and must rely 
entirely on his judgment in estimating the probabilities of 
the hands opposed to his own. He is betting on a known 
proposition against one, two, or half a dozen unknown 
propositions. It is evident that if each player should base 
his own betting on the mathematical chances of his own 
hand being better than any other that might be out, the 
game would be one of pure chance, since he would ignore 
the skill which enables him to recognize the indications 
which guide the good player in judging the strength of his 
opponents. In other words, he would be betting against 


62 


the mathematical chances of his opponents instead of the 
probabilities as evidenced by their play as it progresses 
from step to step. 

In this connection probably nothing better can be said 
than is contained in a quotation from an essay by Edgar 
Allan Poe. / Poe’s fame undoubtedly rests mainly on his 

V 

poetry, but it is true that he was a mental analyst of no 
, mean ability. In treating of the game of whist he wrote : 
. .Proficiency in whist implies capacity for success in 
all these more important undertakings where mind struggles 
with mind. When I say proficiency, I mean that perfection 
in the game which includes a comprehension of all the 
sources whence legitimate advantage may be derived. These 
are not only manifold but multiform, and lie frequently 
among recesses of thought altogether inaccessible to the 
ordinary understanding. To observe attentively is to re- 
member distinctly; and, so far, the concentrative chess- 
player will do very well at whist; while the rules of Hoyle 
(themselves based upon the mere mechanism of the game) 
are sufficiently and generally comprehensible. Thus to 
have a retentive memory and proceed ‘ by the book ’ are 
points commonly regarded as the sum total of good playing. 
But it is in matters beyond the limits of mere rule that the 
skill of the analyst is evinced. He makes, in silence, a host 
of observations and inferences. So, perhaps, do his com- 
panions; and the difference in the extent of the informa- 
tion obtained lies not so much in the validity of the infer- 
ence as in the quality* of the observation. The necessary 
knowledge is that of what to observe. One player confines 
himself not at all; nor, because the game is the object, does 
he reject deductions from things external to the game. He 
examines the countenance of his partner, comparing it care- 
fully with that of each of his opponents. He considers the 
mode of assorting the cards in each hand, often counting 


^3 


trump by trump, and honor by honor, through the glances 
bestowed by their holders upon each. He notes every varia- 
tion of face as the play progresses, gathering a fund of 
thought from the differences in the expression of certainty, 
of surprise, of triumph, or chagrin. From the manner of 
gathering up a trick he judges whether the person taking 
it can make another in the suit. He recognizes what is 
played through feint, by the manner with which it is thrown 
upon the table. A casual or inadvertent word, the acci- 
dental dropping or turning of a card, with the accompany- 
ing anxiety or carelessness in regard to its concealment; 
the counting of the tricks, with the order of their arrange- 
ment; embarrassment, hesitation, eagerness, or trepidation 
— all afford, to his apparently intuitive perception, indica- 
tions of the true state of affairs. The first two or three 
rounds having been played, he is in full possession of the 
contents of each hand, and thenceforward puts down his 
cards with as absolute a precision of purpose as if the rest 
of the party had turned outward the faces of their own.” / 

With some slight paraphrasing, this analysis of whist 
is perhaps as masterly an exposition as could be written of 
the finesse required in the game of Draw Poker, preliminary 
to the betting. /it is absolutely essential to the training of 
a Poker player that he shall study the various indications 
of his opponents’ strength. With all his study he will never 
be able to tell positively what hands are held against him. 
If he could do so the element of chance would be eliminated 
from the game, and he would do nothing but bet on cer- 
tainties. He may, however, acquire considerable skill in 
forming estimates, and the greater his skill in this particular 
the better Poker player is he likely to be. 

We have already classified* the eight considerations 
that enter into the formation of a judgment as to the wis- 


* On page 44. 


64 


dom of a bet. Four of these we have seen to be mathe- 
matical calculations with which the player may so familiar- 
ize himself that he will be able to see, at a glance, what 
chances they present. The other four are points on which 
he must exercise his observation and judgment. 

The player has scanned his original five cards and has 
determined at a glance their actual rank, and the chance 
(varying according to the number of players in the game) 
of any other hand extant being of greater value. He 
knows what the probabilities are as to his bettering in the 
draw, and has seen what money there is in the pot consti- 
tuting the sum against which he has to stake a certain sum 
to obtain the privilege of drawing cards. He should, how- 
ever, consider all the other points mentioned before staking 
his money. 

If he have the age, and no one has raised, he knows 
that the odds offered cannot be changed. By making good 
on his blind he closes the pot. If, however, there are other 
players to hear from after his bet, he will realize that the 
odds against his money will increase with each player who 
comes in without raising. If, however, some other player 
after him shall raise, his money is lost. He has no further 
claim on the pot, though he has still the privilege of making 
another bet at different odds and so acquiring an interest 
in it. What these odds are at any moment, when it comes 
the player’s turn to bet, are easily calculated by the one rule 
already discovered, namely, to compare the amount already 
in the pot with that which the player must put up. No other 
rule applies. The probabilities of a raise by some other 
player can only be guessed at. If the player himself shall 
raise, the rule for determining the odds remains the same. 

In regard to the seventh point in our classification very 
little can be even guessed as to the probabilities of opposing 
hands being bettered until it is seen what cards each player 


65 


draws. Even then there is no mathematical certainty, since 
a good player does not always draw to the strength of his 
hand. If he draws one card he may be trying to improve 
two pairs, or he may have Three of a Kind and be holding 
a kicker to puzzle his opponents, or he may have a four 
Flush, or he may have Four of a Kind and call for another 
card entirely for the purpose of deluding the others. 

Drawing two cards is also puzzling, since the other 
players cannot know whether the attempt is to better Thfee 
of a Kind, or whether a kicker is held up to a pair. The 
safe rule is to credit your opponent with Three of a Kind 
when he calls for two, unless you know his play well enough 
to know that he is in the habit of holding up kickers. Even 
then it is best to be wary. 

If three cards be called for, it is almost certain that the 
one who draws has a pair, since only the most reckless 
players will often pay to draw three to an Ace and another. 
You may therefore judge of the chances of your opponent 
bettering with three cards exactly as you do of your own 
when you draw to a pair. What those chances are has al- 
ready been calculated. And if he draws four cards you 
can tell exactly what his chances are. 

It is therefore to be seen readily that your opponent’s 
draw is only one indication of his strength. It is an im- 
portant one and should be watched closely. To bet against 
another player after the draw without knowing what cards 
he took is playing in the dark. At the same time there are 
many other indications which are also to be recognized by 
a skilful player, as Poe explained, none of which can be 
fully described in a written treatise. The faculty of rec- 
ognizing them can only be developed by practice and by a 
careful study of the individuality of the players in the game. 

Having made the preliminary bets required before 
drawing cards, and having discovered after the draw what 


66 


the actual rank of one’s own hand is, the player will per- 
ceive that he has only two things to consider, instead of 
eight, in forming his judgment as to the advisability of 
betting. He must never lose sight of the actual odds be- 
tween the money on the table and that which he puts up, 
and he must combine his mathematical calculations already 
made with his observation of the play of his opponents in 
making up his estimate of their strength in comparison 
with his own. 

From this point onward, to the final disposition of the 
pot, the game becomes a struggle of individual wit and 
strength among the players. To formulate exact rules as 
to what is and what is not good play under any given cir- 
cumstances is a manifest impossibility. A skilful bluff 
against one player would be mere folly if attempted against 
another. A mastery of the game, beyond the principles 
laid down, will depend entirely on the natural aptitude and 
the practise of the individual. Nevertheless there are many 
of the elements of skill which depend upon a careful study 
of the varying conditions of the game, and such a study has 
been attempted in the following chapters. 

These chapters are articles originally prepared by the 
author for the New York Sun and first published in the 
columns of that newspaper. They are, after careful re- 
vision, republished here by permission. 


Studies 


of Actual Play 



1 




6g 


Elementary Principles. 

I T may be set down as a fundamental principle of the 
game of poker that it cannot be played brilliantly by 
any man who confines his operations within the strict 
limits of mathematical laws. It is unquestionably true that 
the exact mathematical chance in favor of or against the 
winning of any given hand may be figured out in any given 
deal, and it would be possible, if the player holding that 
hand could himself fix the exact amount to be staked on 
it, for him to play a strictly mathematical game. If it were 
practicable to place six players at the table, each one of 
whom knew the percentage of chances of each hand he 
should hold, and if each one should bet or refuse to bet in 
exact accordance with that percentage, the game might be 
reduced to a mathematical basis and would in that case be 
robbed of most of its charm while it would still have all the 
excitement of an intricate calculation in astronomy. 

In other words, there is a fixed limit to the permutation 
even of fifty-two numbers, complicated as it is by the four- 
fold multiplication of values among the units. It would 
be entirely feasible to prepare a table in which each possible 
hand from a Royal Flush down to a seven high of mixed 
suits would appear in rotation, thus making the relative 
value of each apparent to the eye. The value of such a table 
would be considerable to the beginner, since he could deter- 
mine at a glance how high up among the possibilities each 
hand stood. No one ever did or ever will prepare such a 
table, however, since the player's first lesson is to learn the 
comparative value of all hands, and the sequence is simple 
enough to be mastered without the aid of diagrams. 




70 

Supposing this table to be prepared, however, it be- 
comes a simple though a tedious operation to calculate the 
chances of each one of the other five players holding a 
hand of equal or superior value. A separate calculation 
on each hand before and after the draw is involved in each 
case, each one varying according to the draw, but all being 
calculable from the same table, on the same principles of 
permutation. The mathematical chances of each hand can 
therefore be reckoned to a fraction, and if it were worth 
while to reduce the game of poker to the level of the me- 
chanical operations of a nickel-in-the-slot machine, it might 
be done. 

For two reasons, however, it will never be done. The 
first of these reasons is that the calculation would be al- 
most incredibly tedious, while the result to be obtained 
would be of trivial value, and the second is that the more 
important elements of the game so completely overshadow 
the mathematical quality of it that such a calculation is 
practically unnecessary. 

It is nevertheless a necessity for a poker player to have 
as a beginning of his knowledge of the game a clear con- 
ception of the frequency with which different hands may 
be expected. The best way, practically, to obtain this con- 
ception is by long-continued play and close observation. 
The player who should begin with a mathematical calcu- 
lation of the probabilities would be so confounded and con- 
fused by the constant contradictions of actual play that he 
would not only be at a loss to know how to govern his bet- 
ting, but he would almost inevitably lose sight of the real 
probabilities of the sitting in which he might be. 

To illustrate: It is by no means an uncommon thing for 
the same party of six to play together at poker for a dozen 
sittings without having Four of a Kind held once in the 
entire series. And, on the other hand, it is not unusual for 


7 1 


Four of a Kind to be held twenty-five or thirty times in 
another dozen sittings of the same party. They might 
play together for a year and not have a single Straight 
Flush, and in the following month it might very probably 
be seen half a dozen times. All this is by no means a contra- 
diction of the principles of permutation or the doctrine of 
chances, but it shows that apparent contradictions are so 
frequent that a strict application of those principles is in- 
compatible with sound play. 

It is easy to quarrel with the word “ luck,” and it is 
easy to demonstrate on paper that in the course of a hun- 
dred million deals, for example, just so many Straight 
Flushes will appear, just so many Fours, and so many 
Fulls, Flushes, Straights, etc. The theory may be sound 
enough, and it is much easier to concede it than to attempt 
to prove or disprove it by keeping account of the full series. 
The fact remains, however, that the frequency with which l 
certain hands appear varies so greatly at different sittings 
that the mathematical calculation is forced to the rear. It 
remains a factor in the chances, but there is also the factor 
which we call luck, for lack, possibly, of a better word, and 
which is actually more potent than the strictly mathematical 
probability. 

There is actually developed in the skilled poker player 
a sort of sixth sense, consisting of a perception of chances 
dependent on what he calls luck, no less than on the mathe- 
matical probabilities, and this sixth sense is one of the 
essential qualifications of a really good player. To possess 
it, he must have a fair comprehension of the mathematical 
laws, which, as was said, is better obtained by actual play 
than by the study of permutation, and he must also have the 
instinctive perception, which is by no means to be described, 
of the presence of a “ run of the cards.” This is a quality 
that may be derided, and even the existence of it may be 


denied by mathematicians, since it is founded on no laws 
that have ever been formulated, but its actual operation is 
too frequent and too well defined to admit of any doubt in 
the minds of experienced players. 

This perception of chances, while it is here set down 
as an essential qualification of a good poker player, is by 
no means the only qualification that is essential. Fully as 
important as this, if not more so, is the ability to gauge the 
play of his opponents. It must be remembered that no 
hand can be held, short of a Royal Flush, which cannot be 
beaten, and while a player may perhaps be justified in 
backing a very strong hand, like Four of a Kind, for ex- 
ample, as if it were invincible, yet the good player will never 
lose sight of the chance that there is against him. An ex- 
treme illustration of this would be the case of a man holding* 
four Aces against a single antagonist who has drawn three 
cards. The most natural thing imaginable would be for 
him to bet all he had on his hand, providing his antagonist 
were strong enough to stay, but this, while it would un- 
deniably be sound play from a gambler’s standpoint, would 
not be theoretically perfect poker playing. The distinction 
may seem arbitrary and even farfetched, but it actually 
exists. The poker player, while he must be able to calculate 
the chances in his favor to a nicety, must also keep in mind 
the chances against him, and to eliminate these latter 
chances altogether when they are present, is not good poker, 
theoretically. 

The player, then, has a known quantity — his own hand 
— to back against an unknown quantity — the hand or 
hands that are out against him. His own hand has a posi- 
tive and a relative value. Its positive value is determined 
by its position in the supposititious table in which are set 
down all the hands that can possibly be held, together with 
a calculation of the frequency with which they appear in 


) 


I 


73 

an indefinite series of deals. This positive value he can 
determine at a glance. The relative value he can only judge 
of by means of a complex process of reasoning. Into this 
problem enter many factors. The first thing he has to 
judge from is the draw. Knowing how many cards each 
of the other players drew, he can estimate the probabilities 
as to what they held before the draw, and his experience 
has shown him how to calculate the chances of their hav- 
ing filled their hands or bettered them. Then, if he has 
the last say, he can also form some estimate from the nature 
of their bets. 

Up to this point, Draw Poker may be compared with 
almost any other game of cards. The rules of the game, 
when they are once understood, seem very simple, for they 
are founded on a few cardinal principles, and when these 
are thoroughly mastered each rule commends itself to the 
player’s mind as being logical and well adapted to the main- 
tenance of these principles. 

But up to this point, as was said, Draw Poker is merely 
a game of cards, and this play is reducible to rules and 
methods as arbitrary as those which govern whist or any 
other game. In the case of Poker, however, the entire 
framework of the game, as a game, is merely rudimentary 
knowledge, necessarily to be acquired, it is true, but only 
preparatory to the exercise of the various faculties which 
are brought into active operation in the actual play. 

In other words, the cards are the weapons, and the rules 
of the game are merely the code that governs the contest 
in the great game of Draw Poker, which is really an in- 
tellectual struggle. The actual play calls for much more 
than a knowledge of the cards, of the value of hands, and 
of the rules of the game, for it is in the betting that the 
skill is displayed, and the betting calls for accurate judg- 
ment, quick decision, caution, daring, and cool nerve. The 


74 


player must not only judge of what he considers good play 
on his own part, but he must know what every other player 
considers good, and must make his estimate of their play a 
fundamental part of his own. 

It is often said that nobody can win at poker unless he 
holds good cards, and there is some truth in the saying, 
for it is hardly conceivable that any player could continue 
a series of bluffs indefinitely, without losing more in a long 
run than he would win from time to time. A grand coup, 
however, which may sometimes be made on the pretence of 
holding cards when one holds nothing of importance, is 
always among the possibilities of poker, and this fact not 
only lends fascination to the game, but also sustains the con- 
tention that it is not merely a card game. 

Again, there is a common belief that the unskilled be- 
ginner at the game is more likely to win at his first game, 
or his first few games, than the old, experienced player, and 
this alleged fact has been cited as an argument by those 
who claim that poker is more a game of luck than of skill. 
The best answer to that argument that has been made was 
the reply given to a tyro who boasted of his success in 
Wall Street. “ I shall never go back into regular business/' 
he said, “ for I can make more in the Street in a day than 
I could make in a year in my old office/’ “ Yes," said 
his wise friend, “ that’s easy. Anybody can make more in 
a day in Wall Street than he can make in a year in business. 
The thing to do, however, is to make more in a year." 

So, in poker, no man may call himself a player until 
he shall be able to hold his own, not once or twice, but in 
a long series of sittings with experienced players. It may 
be that no one can win forever without cards, but it is 
unquestionably true that one can lose forever, even with 
winning hands. The cards are important, but there are 
other elements of the game of at least equal importance. 


75 


The Problem of the Draw. 

A N expression commonly used by poker players is “ It’s 
all in the draw,” the meaning of which is that a 
player’s chance of taking the pot depends entirely 
on what cards he may get when drawing to those which 
he selects to hold, out of the original five which he receives 
in the deal. Properly understood, the saying is one to which 
no serious objection can be made, for it is certainly true that 
the character of the hand he holds is liable to be entirely 
changed by the draw, and the most insignificant pair may 
be transformed to Four of a Kind, while it is only in the 
case of a pat hand that the player can tell before the draw 
what he has to rely upon in the final betting. 

Nevertheless, as the saying is commonly used it is delu- 
sive, and provocative only of wild and unjustifiable play. 
It is to be remembered that while a lucky chance in the 
draw may transform a worthless hand into an almost sure 
winner, an unlucky draw will leave the player without the 
chance of winning and minus the amount he has put in 
the pot, and, moreover, each player in the game has the 
same chance of bettering. “ It’s all in the draw,” is a re- 
mark most frequently made by some player who is seeking 
to justify himself in making an unjustifiable play. 

Taken in its best sense, however, it expresses one of 
the cardinal principles of the game, and one of the first 
efforts of the player, after he has mastered the rudiments 
of the game, should be to exercise proper discretion in the 
draw. In undertaking to master this, he has to consider 
that the conditions vary according to the amount already 


7 6 


in the pot, the number of players, the position he occupies 
at the table with relation to the age, and somewhat accord- 
ing to the run of luck he may be in. 

Beginning with the simplest proposition, it may be asked 
what hand justifies a player in coming in, when there are, 
say, six players in the game, and it is a straight deal — no 
jack-pot. The age man has made his ante of one white 
chip, and the learner sits next to him. There are four 
other players to hear from before the age is to fill or pass 
out, and he therefore has to consider first his own hand 
and then the five possibilities against him. His own hand 
lie knows at a glance. The five other hands he has no 
means of estimating, excepting on the basis of mathematical 
probability. It is therefore a simple question of how far 
up in the table of possible hands his own hand ranks, which 
must decide whether it is wise or foolish for him to pay 
two white chips for the privilege of drawing cards. He 
must remember, also, that after having paid those two, he 
is liable to be obliged to see any raise that may be made 
after he comes in, or to sacrifice the two he has chipped in. 

Most good players have a simple rule governing their 
action under these circumstances. Perhaps it may be said 
that all good players have such a rule, but there are many 
successful players who vary the application of the rule ac- 
cording to the luck in which they find themselves at the 
moment. The rule most commonly followed, because it is 
in accord with the table of chances, is not to come in with- 
out a fair-sized pair to draw to. Cautious players throw 
down any hand that contains less than a pair of tens, unless 
it be a Four Flush or a Four Straight. Anything better 
than two tens is universally held to be a good risk, but 
bolder players will come in on a smaller pair, even as low 
as deuces, holding that there is an equal chance of getting 
three of a kind, whatever the pair is, and that three deuces 


t 


77 

is worth a play. This seems plausible, but the argument 
against it is that there aie five possibilities against the 
hand, and that few players will come in on so small a hand ; 
therefore each hand in opposition is likely to be larger. The 
player sitting next to the age who comes in on less than a 
pair of sevens or eights is properly to be classed as bold, if 
not rash. 

An analysis of this statement will show that the ele- 
ment of rashness lies in entering into competition with five 
other players, all of whom are yet to be heard from, with- 
out having a hand stronger than, say, sevens. Of course 
the next player, the first having passed out, will have only 
four antagonists to look out for, and if he shall elect to 
go in on sevens he is less rash. Exactly how much less, 
it is impossible to say positively, since the hands yet to 
hear from are still unknown quantities, but a rough work- 
ing rule has been formulated by which a player who fixes 
a pair of eights as the lowest on which he will venture 
when he sits next to the age will consider sevens suffi- 
cient if he occupies the second seat, sixes if he occupies 
the third, fives if he occupies the fourth, and any pair at 
all if he has only the age man to play against. And, of 
course, it is to be remembered that, as the deal passes, 
each player occupies the different seats in rotation, so that 
the two things he has to consider are the seat he occupies 
and the cards he holds. A conservative play, as nearly safe 
as poker can ever be said to be safe, would be to start 
with tens in the first seat, even with seven players in the 
game, and reduce the size of the pair with each removal 
from the age in rotation, but never go in on less than a 
pair of fives unless he has the age. In that case, having 
already been obliged to chip once, he would have only one 
chip more to venture and would fill his ante even though 
he had onlv deuces. 

j 




73 


It must be remembered also that before the draw a 
Four Flush or a Four Straight is a more valuable hand 
than a small pair. This is not because the chance of bet- 
tering is greater, but because the hand, if filled, becomes 
a strong one. Theoretically, the Flush should be filled 
oftener than the Straight, since there are nine cards out 
of the forty-seven which the player has not seen, any one 
of which will complete his Four Flush, while there are only 
eight of the forty-seven which will fill a Four Straight. 
And in drawing to a Straight, both ends should be open. 
Drawing to an Ace, Deuce, Trey, Four, or to a Jack, Queen, 
King, Ace, is the same thing as drawing to an intermediate 
Straight, since there are only four cards in the forty-seven 
which will fill, and the chance is too small to justify a draw 
with odds of no more than six to one against the player's 
ante. 

If there were no other situations than those already de- 
scribed it would always be, as has been seen, a simple 
matter to decide whether to draw cards or not. As a mat- 
ter of fact, however, there are many complications con- 
stantly arising, each one of which varies the problem. The 
first of these is the raise before the draw. Supposing some 
one to have raised before the player has his say, there is 
a question to be decided before coming in, whether the raise 
was made on the strength of a good hand, or whether it 
was a bluff, pure and simple, or whether it was made 
for the purpose of frightening out as many players as 
possible. If there be good reason to suspect a bluff, it 
is good play to follow the rule already decided on, and 
come in on a pair or better, precisely as if no raise had 
been made. The chance of improving the hand is not 
affected by the raise, and although the cost of coming in 
is increased the odds remain the same, providing no one 
else is kept out. If the player believes, however, that the 


79 


raise was not a mere bluff, but was made on the strength 
of a good hand, it would be counted good play to throw 
down anything less than two pairs, unless it were a Four 
Flush or a Four Straight. 

Still another situation arises when the raise is made after 
the player has put up his ante. It is to be supposed if he 
has done this that he has cards to draw to — a pair or 
better — and having his money up he must decide whether 
his chance is good enough to justify paying more money 
before he can draw. In making this decision he has to 
consider his own hand, the number of hands out against 
him, and the probable strength of the player who made 
the raise. This last, of course, he can only judge by guess- 
ing, and the only guide he has to his guess is his knowl- 
edge of the way the other player usually plays. Each suc- 
cessive raise before the draw, if there be more than one, 
theoretically exposes increased chances against the player, 
but, on the other hand, each time he sees a raise the odds 
of the bet are changed so that he may be justified in taking 
a longer chance. 

This statement about the increase of odds requires a 
word of explanation. In a game of seven players, pro- 
viding all come in, the odds before the draw stand at 6 to 
i against each player when the pot is completed, but there 
are constant variations in that before the completion. The 
only correct way, or safe way, to figure is that the money 
already put in is gone, and the odds against each player 
every time he makes an addition to the pot are measured 
by the proportion which that particular contribution bears 
to the whole amount in the pot. To make this clear, desig- 
nate the players by letters. A deals. B antes. If C comes 
in he gets only i to 2, D gets 3 to 2, E 5 to 2, F 7 to 2, 
and A 9 to 2. If B then fills he is getting 11 to 1, since) 
he can no longer count the ante as his own money. This 


8o 


explains clearly why B can afford to draw to a much smaller 
hand than C can. 

But supposing A, when it comes his turn, not only goes 
in with the required ante, but raises it five white chips. 
The figuring must all be done over, and each man must 
decide anew as to the advisability of drawing cards, keep- 
ing in mind the hand he has to draw to, the odds he gets 
on the bet he must make before he can draw, and the 
chances of the five hands out against him, with the ques- 
tion open as to whether A has a strong hand or is bluffing. 

B then gets odds of 17 to 6 if he fills and sees the 
raise. C gets 22 to 5, D 27 to 5, E 32 to 5, and F 37 to 5. 
But if all stay, by the time it has reached F he will have 
to face the probability of several strong hands being out, 
and though the odds in the bet are greatly in his favor, the 
chances against him are heavy unless he also has a strong 
hand. And in the meantime there may have been another 
raise, and new odds have to be figured each time. 

Thus far we have only considered the case of an ordi- 
nary pot. When we come to the jack-pot we find the con- 
ditions entirely different, though the principles remain the 
same. The odds to be figured are different, and are much 
greater in favor of coming in, so that a player is justi- 
fied in drawing to smaller cards than in an ordinary pot, 
even though it is certain that the opener has Jacks or 
better. These odds, again, vary according to the amount 
the pot has been opened for, and on how many players have 
come in before he has his say. There is also the prob- 
ability to be estimated of a raise before the draw, so that 
only the man on the right of the opener or of the last who 
has raised can know positively what odds he will have to 
play. The only reason why it is good play to come into 
a jack-pot on a smaller hand than it is wise to back in an 
ordinary pot is that the odds in the betting are better, for 


8 1 


it must always be remembered that the player is betting 
against the whole pot, regardless of how much he may 
have put into it already. Otherwise the fact of the opener 
certainly having Jacks or better would indicate the wisdom 
of staying out with a smaller pair. 

“It is a good player who knows when to throw down 
a good hand.” This is a saying which is often heard, and 
the foregoing analysis of the odds which can be figured, 
and of those which can only be guessed at, makes the mean- 
ing of the saying clear. At all events, enough has been 
said to show how a player who has studied the tables suf- 
ficiently to know the chances of the draw can decide as 
to the wisdom of drawing cards. That is, the wisdom on 
the basis of mathematical computation. The further propo- 
sition that it is always wise to back your luck is seldom 
disputed by experienced players, so that it is held good 
play, or at least justifiable, to draw to a single card, or 
even a Three Flush or an intermediate Straight, if the player 
is sitting in exceptional luck. The question of how far to 
press the luck is practically answered by each player ac- 
cording to his temperament, and since a run of luck in 
itself consists of a series of contradictions of the law of 
mathematical probabilities, no positive judgment can be 
passed, except in extreme cases. The fact that no run of 
luck can be expected to continue indefinitely should keep 
the player on the watch for the first indication of its turn. 

The importance of studying the chances of the draw 
and the wisdom of passing out on poor cards are unques- 
tionable. As a matter of experience it can be stated pos- 
itively that more money is lost at poker in the long run 
by paying to draw cards when the chances are against the 
player than is lost by betting on hands after the draw. In 
the betting, unless one's luck is persistently bad, he will 
win sometimes, and will have a chance to recoup his losses, 


82 


but the player who chips in constantly without holding the 
cards to justify his ante has no probability of recovering. 
It is true that he will sometimes make an extraordinary 
draw, but he will not win enough on such a hand to pay 
for his frequent chipping in without results. 

But after having arrived at an understanding of when 
it is wise to draw and when it is still wiser to lay down, 
the learner has still to study how to draw. In this it is 
only possible to lay down general rules, because the game 
is one of such complexity as to require the disregard of 
all rules of play on occasions. Or rather, the grand prin- 
ciple being always regarded, the situations of the game are 
so varied as to call for a frequent disregard of general rules. 

Good players generally “ draw to the strength of their 
hands.” That is, a man holding a pair will draw three 
cards ; holding three of a kind he will draw two, and hold- 
ing two pairs he will draw one. No good player, how- 
ever, holds himself always bound by this rule, since he may 
at times wish to deceive his antagonists. And many fairly 
successful players habitually vary this play by holding an 
Ace with a pair, believing that the chance of making Aces 
up on a two-card draw is better than the chance of three 
of a kind on a three-card draw. Opinions differ as to the 
wisdom of this, but the general opinion is against hold- 
ing up a “ kicker,” unless the player wishes to convey the 
impression that he has three of a kind. Obviously if he 

holds up a kicker frequently, he will not convey the im- 

* 

pression to those who are familiar with his style of play. 
This variation from mathematical play, like standing pat 
on an incomplete hand, is nothing more or less than a 
bluff and is only justifiable as a means of puzzling the 
other players and so destroying their confidence in their 
own hands. 

There is one contingency in which a good player will 


33 


sometimes deliberately break this rule of drawing to the 
strength of his hand. He may have stayed in a pot, be- 
lieving that his hand is as good as any that is out against 
him, but when it comes to the draw he may see from the 
number of cards the others take that they all have better 
chances than he. Supposing he has two pairs. If he draws 
one card he has four chances in forty-seven of making a 
Full, and if that Full be a very small one he might feel 
no confidence in it. If, then, he discards one pair out of 
his two, he will have a very much smaller chance, but still 
a chance, of getting four of a kind. It is one of the long- 
est shots to be played, but if he is convinced that his chances 
with a small Full are worthless, he is justified in taking 
even that chance. 

Another case which more often occurs will show the 
wisdom of disregarding this general rule on occasions. It 
frequently happens that a player will hold a good pair, say 
of Aces, and feel a reasonable confidence in them before 
he has seen the other players* draw. It may be, however, 
that one or two other players have stood pat, another has 
drawn one card and another has drawn two. In such a 
case a single pair is a poor hand to draw to. There is, 
of course, a chance of making three of a kind or two pairs, 
which would be a worthless hand. There is also a possi- 
bility of a Full and a still more remote possibility of four 
Aces, either of which would be worth betting on. It may 
happen, however, that by discarding one of his Aces he 
will have a fairly good chance of making an Ace Flush, 
and his judgment may be that an Ace Flush would be 
worth playing. In such a case it would be good play to 
split the Aces and draw to his Four Flush. Otherwise a 
pair of Aces is esteemed the better hand to draw to. 

Enough has been said to indicate that in the draw, as 
well as in every part of the play, the game of Draw Poker is 


8 4 


played best by the man who best knows when to disregard 
the general rules of good play. But the beginner, seeing 
the rules frequently disregarded, is likely to make the mis- 
take of underestimating the importance of rules. In no 
other part of the game is he more likely to make this mis- 
take than in drawing. He may see a good player some- 
times draw to an Ace or even take five cards and occa- 
sionally win a pot as a result. The natural effect is to 
encourage the poor player to do the same thing, but if he 
does, he will almost invariably suffer, for he will not know 
enough of the game to understand when such play is ut- 
terly indefensible and when it is justifiable. The only safe 
course, therefore, is first to master the general rules and 
afterward try to become familiar with the conditions that 
justify a departure from them. 


*5 


The Limit. 

O NE of the essential characteristics of the game of 
poker, and probably the one above all others which 
tends to make it the most fascinating of all games 
to those who play it long enough to become really familiar 
with it, is the opportunity it offers, at almost every turn, of 
forcing one’s antagonists into new play. Whether there 
be two or seven players in the game, each, as it comes his 
turn, can inject a new problem for the others to solve, and 
so make his individuality felt, quite apart from the real 
value of the cards which he may or may not be obliged 
to show down at the conclusion of the play on each hand. 
This seems to make the game unique among card contests, 
since it is entirely feasible to win without winning cards, 
a thing which is not possible in any other game, and this 
peculiarity really raises the game to a higher level than 
that of any other card game, without disparagement to 
those which call for a thorough knowledge of card values 
and combinations. 

It is therefore necessary for the student of Draw Poker 
to pay close attention to the influence which the limit ex- 
erts on the character of the game. Strictly speaking, the 
limit, whatever it may be, is in contradiction to the real 
genius of the game. The ideal game of poker in theory 
would be one that would be played by six or seven game- 
sters, each of whom had an unlimited supply of money 
which he would be entitled to wager without restriction at 
any stage of the game. In other words, a game played 
with no limit would afford the fullest opportunity for the 


86 


development of all the fine points of the game, and for 
the display of all the qualities which make up the really 
first-class poker player. 

The necessity for an unlimited supply of money behind 
each player in the theoretically perfect game becomes ap- 
parent when we consider that, practically, there must be 
a limit to every game of poker, since no man can have 
unlimited money. The limit that obtains practically, there- 
fore, in every game is fixed by the invariable rule that 
each player may have a show for his pile. Were this rule 
to be set aside, it is obvious that the man with the longest 
purse could easily win at every sitting by the simple ex- 
pedient of betting more money than his antagonists had. 

In the nature of things, therefore, there is and must 
be a limit in every game of poker, even if that limit be 
fixed on each bet at the entire amount which any player 
has to bet. Really, unlimited poker might perhaps have 
been enjoyed by the gods on Mount Olympus had they un- 
derstood the game, but as a matter of fact, it would require 
the lapse of eternity to determine the winning of a single 
pot if it happened to be contested by two equally confi- 
dent and obstinate players; so that taking the limit off ab- 
solutely would destroy by reaction the interest of the game, 
while theoretically it would make the game perfect. 

Since there must be in practice, therefore, a limit, this 
limit, whatever it is, is always fixed by common consent 
among the players. No man can be forced to play beyond 
the entire amount of his earthly possessions, and if the 
game involved any possibility of more than that, no sane 
man would play it, unless, indeed, he played with men 
poorer than himself, and in that case the game would be- 
come systematized grand larceny. And since no rational 
man can be expected to sit down to any game that is likely 
to call for a risk of all his possessions, the practice com- 


87 


monly is to fix the limit at such a figure as represents as 
much as any player is willing to risk on a single bet. The 
unlimited game, so called, is sometimes played, though not 
frequently, and it is really not unlimited, since any player 
may at any time bet all he has and declare that amount to 
be the limit so far as his hand is concerned. 

Leaving this kind of game out of consideration, it may 
be said that there are two ways of fixing the limit beyond 
which no player is permitted to force his antagonist to go 
in a single bet. One is to agree upon some sum, what- 
ever it may be, which shall be the largest single bet per- 
missible, and the other is to play table stakes. This term, 
though commonly well understood among players, requires 
a few words of explanation. In playing table stakes each 
player displays in front of him the entire amount for which 
he desires to play, either in money or chips, as may be 
convenient. Thereafter during the time he continues to 
remain in the game he may withdraw a portion of this 
money or add to it, as he sees fit, but he may not do this 
while a pot is being played for, if he is one of the con- 
testants for that pot. And he may at any time, when it 
comes to be his turn to play, bet the entire amount in front 
of him, or any portion thereof, as he sees fit, but he can- 
not be forced to bet more than he has in front of him, 
nor will he be allowed to do so, excepting that, with the 
consent of the other players, he may add to his pile if he 
desires to play further on his hand. If any one objects 
he is not at liberty to do this, and if at any time he bets 
all he has, that bet becomes the limit in that pot, so far as 
his interest in it is concerned. If any of the other players 
desire to bet more on their hands they can do so on the 
side among themselves. 

This statement of the rule governing table stakes is 
given here merely for the purpose of showing the differ- 


88 


ence between this and the more usual limit game. It is 
evident that the table-stake game affords a freer oppor- 
tunity for the display of bluffing or skill in play than the 
so-called limit game, since the player may force the play 
harder whenever he desires to do so, either for the sake 
of winning larger stakes or for the purpose of keeping as 
many antagonists as possible from contesting the pot, which 
he may desire to do if he has no great confidence in his 
hand. The table-stake game is preferred on this account 
by expert players, as giving more scope for the exercise 
of their skill and a better chance for quick play and large 
winnings. 

The timid or inexperienced player will do well to con- 
fine himself to the limit game, at least until he has mas- 
tered the principles of poker and learned by practice to es- 
timate the probabilities of the game and his consequent 
chances of winning or losing on a given hand under given 
circumstances. While it is true that he has not the same 
opportunities for brilliant play, he is better guarded against 
the dangers of rash play, and at the worst is likely to , get 
a longer run for his money. Among players, also, who 
indulge in the game for the pleasure of play rather than 
for the possibility of gain, the limit game is commonly 
preferred. 

In theory, of course, when a limit is fixed on the size 
of a single bet, there will be limit bets only on occasions. 
That is, the ordinary betting will be for smaller amounts, 
and only when the occasion calls for an implied assertion 
of a strong hand will the full amount permitted be pushed 
forward as a single bet. In practice, however, the tendency 
is generally toward limit play, especially when the limit is 
small. Of course, what would be a small limit among 
well-to-do players would be desperate gambling among 
poor men, and as there is no arbitrary figure to represent 


8 9 


the difference between wealth and poverty, no standard can 
be set up as representing a large or a small game. 

It may be assumed, however, that for people in ordi- 
nary circumstances who play poker for pastime rather than 
for gambling, anything over a fifty-cent limit means a 
serious game, if not, indeed, real gambling. As was said, 
this is a purely arbitrary distinction, and a fifty-cent limit, 
while it seems insignificant to many, is a very large game 
to others. Generally speaking, an ordinary evening’s play, 
from three to five hours in duration, among fairly matched 
players, is likely to mean, at the outside, a loss or gain of 
not more than fifty times the limit. A greater loss or 
gain may frequently be made, but it would be considered 
unusual. One who has no mind to lose more than $20 or 
$25 in the course of an evening, therefore, would do well 
to avoid a game where the limit is higher than 50 cents. 

It is of the last importance for every player to learn, 
and thoroughly to understand, how the limit on a single 
bet necessarily restricts him in his own play and at the 
same time curtails his chance of being able to calculate 
the chances from his opponents' play. If the limit be a 
small one, as was said, the tendency of a majority of play- 
ers is to bet the limit each time. Thus, in a ten-cent limit 
game, where the white chips are valued at one cent, the 
red at five and the blues at ten, the player who bets a 
white chip is usually either putting out a coaxer in the 
hope of getting a raise, or he is fearful of a raise and dis- 
inclined to venture more than he is forced to on his hand. 
The bet of a blue chip is no more than he would naturally 
venture on a hand with any fair chance of success, and is 
therefore no indication of either a bluff or a good hand. 
When the limit is higher, say $1 or $2 or more, a com- 
paratively small bet is more common, and as the game has 
more of what may be called elasticity, there is a better 


9 ° 


opportunity of studying the play of one’s opponents, and 
also a better opportunity of varying one’s own play in 
accordance with the cards actually held or according to the 
theory of a bluff. 

Speaking broadly, therefore, it may be said that the 
limit which gives each player a show for his pile when- 
ever he sees fit to venture it all and demand a show-down, 
is the one restriction that makes poker practicable as a 
game among any but multi-millionaires and that without 
that restriction no one would ever be likely to play it. And 
further, that each narrowing restriction on the game from 
the rule of table stakes down to the five-cent limit, which 
is the smallest game played unless the chips are valued at 
less than a cent apiece, serves to eliminate some of the 
charm of the game, but at the same time renders it pos- 
sible for more people to play it. Thus there are thousands 
who can play and enjoy the game with a small limit who 
could not afford to play if the limit were a dollar or more. 
Even with a small limit, however, it is possible not only 
to learn the game well, but also to become sufficiently ex- 
pert to master the principles thoroughly, excepting as to 
the value of the bluff. That, as was explained, cannot be 
brought into play with any effect if the limit be small, and 
the player who is accustomed only to the limit game is 
therefore obliged to do considerable studying when he be- 
gins to play table stakes. While the rules of the game 
remain unchanged in any other particular, the greater free- 
dom of the table-stake game is apt to confuse and even 
to terrify the player who has never before played except- 
ing with a bet limit. A greater amount of courage and at 
the same time greater caution are called for and the two 
involve the necessity for a greater degree of skill. 

A discussion of the limit in poker would not be com- 
plete without a reference to what is called ' Progressive 

\ 

\ 


9i 


Poker. This is a game not often played in this country, 
though it is said to be comparatively common in England. 
It is not played anywhere excepting among those who are 
eager for the excitement of high play, and it seems well 
adapted to produce that excitement, for the play cannot 
by any degree of caution be made small, while at the same 
time it can be made as high as the most enthusiastic player 
can possibly desire. 

The limit in this game is not a restriction of the bet 
to a given amount, but a rule against betting less than a 
given amount. To illustrate : Six men are playing, and 

A has the age. He antes, say $i. B looks at his cards 
and if he desires to play he must put up $2. Up to this 
point the game is the regular one. C, however, cannot come 
in by paying $2. If he thinks his cards justify a play he 
must put up $4. D in turn must put up $8, E $16, and 
F $32. If, then, A desires to play it costs him $63 in 
addition to the one he put up originally, and each player 
in turn must make his ante good to the extent of $64 be- 
fore he can draw cards. I11 that case, $1 being the original 
ante, if all six should come in and no raise should be made 
beyond the compulsory doubling each time, there would be 
$384 on the table before the draw. 

It must be remembered, however, that each player, when 
it comes to be his turn to bet, may raise if he chooses, 
though not less than the amount he is called upon by the 
rules to bet if he bets at all. Thus C, when he comes in, 
must put up $4 or drop out. If he desires to raise he may 
do so, but his raise must be at least $4. If he does not 
raise, but simply comes in, and D wishes to raise he must 
raise not less than $8. It will be seen, therefore, that in 
case all the players make good, each raise made by any 
one of them means that the pot is at least doubled. Even 
if some drop out, as some would be likely to do unless the 


9 2 


game were played in Bedlam or some extraordinary hands 
had been dealt, the geometrical progression in the betting 
makes important money to be played for, even if only three 
or four of the players stay in. 

When the betting begins after the draw the same rule 
obtains as to a raise. A player may either see the amount 
put up by the bettor before him, or he may raise, but if 
m he raise he must raise the full amount of the bet, or in 
other words double. This would seem to be sufficiently 
hard play to satisfy the most desperate gambler, and it is, 
as a matter of fact, much more desperate play than is 
often seen on this side of the Atlantic, but there is a way 
of playing it that makes the game even more exciting and 
the stakes even larger. 

This last variation is to make it compulsory on eacli 
player, instead of merely seeing the bet that has been made, 
to double the stake or drop out. Thus if after the draw B 
should bet $i, C must either lay down his cards or bet $2. 
D has also, of course, the privilege of resigning, but if he 
stays it costs him $4. And this doubling is kept up until 
all have resigned but two. Then, when a player has only 
one antagonist left, he has the privilege of calling. 

It will be readily seen that no such game as this would 
ever become popular excepting among the most desperate 
gamblers. As a matter of fact the author has never known 
of its being played excepting in two or three cliques of the 
fastest men in London, to whom money was as nearly val- 
ueless as money ever can be. It is possible that it is played 
elsewhere, but the only way in which the average man could 
ever hope to be able to play it would be by making the chips 
of almost infinitesimal value, or by the exercise of such 
self-control as would lead him to stay out of every pot 
unless he had an extraordinary hand. That method of play 
would, however, tend to make the play monotonous in- 


93 


stead of exciting and the game would thereby defeat itself 
and nullify the very object of increasing the excitement. 
Progressive Poker may therefore be properly omitted in 
commenting on the limit, and the word limit may be taken 
in its ordinary sense as a rule forbidding the player to bet 
more than a specified amount, not a rule compelling him 
to increase a bet or stay out. 

The limit, then, while it unquestionably seems to restrict 
the game of poker in many ways, not merely by confining 
the probable losses and gains of the play, but by eliminat- 
ing much of the fierceness of that struggle of wits which 
makes the game so fascinating, has also served to place 
poker within the reach of multitudes of players who would 
not be able to enjoy it if it were played according to the 
original scope of the game. It is true that if a player sit 
between two others who raise in turn he is likely to be 
tempted to continue the contest even when he does not 
reckon his own hand to be worth a raise, but that is one 
of the positions in which he needs to exercise that self- 
control which leads a player to lay down any hand, how- 
ever good, rather than bet more than he really believes it 
to be worth. That self-control is one of the first things 
to cultivate, for without it no one can hope to be a good 
poker player. 


v 


94 


Personality in Poker. 

T HE first disagreeable surprise the beginner is likely to 
encounter in learning the game of poker is, of course, 
the discovery that the hand he fondly imagined was 
the best one out in a given deal is in reality outclassed by 
some other player’s hand and that the pot he deemed as 
good as won is the lawful spoil of that other player. This 
particular form of disappointment, however, is likely to be- 
come so familiar in a short time that it will occasion no 
shock. The most optimistic player does not expect to win 
on every good hand, and he will soon become accustomed to 
the thought that anything less than a Royal Flush is liable 
to be beaten without the implication of even a suspicion of 
foul play. 

The next thing in the game which is likely to fill the 
player’s mouth with ashes and his soul with a fierce long- 
ing to go out and kick a few stars out of the firmament 
is the discovery that he has overestimated his antagonist’s 
strength and has relinquished his own good cards because 
he had not the courage to back them, when in reality his 
opponent was betting on eight high and plenty of nerve 
or something equally absurd. It is doubtful if even the best 
player that ever lived could entirely overcome the chagrin 
that follows the realization of having made such a play. As 
time goes on and he gains experience the good player will 
learn to control himself so as to give no expression to his 
feelings, but even time and experience will hardly serve to 
mitigate the contempt he will feel for himself at having been 
bluffed. 


% 


95 


The experience, nevertheless, is a part of his education 
and may be made valuable to him if he have the gifts of 
observation and analysis which will enable him to study un- 
derstandingly the personality of the man who has success- 
fully carried out the bluff that beat him. The recognition 
and comprehension of the bluff constitute the higher edu- 
cation in poker, and without some degree of this knowledge 
no player can hope to attain the third degree. And as the 
first element of success in the difficult art of bluff is the 
personality of the player, the best safeguard a player can 
have against the chances of being bluffed lies in his ability 
to gauge the personality of those playing against him. 

This necessity for an understanding of human nature 
generally and of individual character in particular is what 
raises poker above the level of other card games and justi- 
fies the assertion of its admirers that it is very high-class 
training for the man of the world whose affairs lead him 
into close and frequent contact with all sorts and conditions 
of men. For it is to be remembered that this study of per- 
sonality is almost a necessary part of the game, even in 
such plays as are made strictly on the merits of the cards, 
with no effort at bluff on the part of any participant. It 
is fully as important to know when your opponent is not 
bluffing as it is to know when he is. Indeed the former 
feat is sometimes classed above the latter, since it leads to 
the highest achievement of the game, namely, the refusal 
to back a hand which, according to the mathematical 
chances of poker, calls for heavy betting. 

To illustrate the importance of this, it is worth while 
to quote here a story told to the author by a Yale student 
who learned the game at college: 

“ Our crowd had played together for quite a while,” 
he said, “ and I had come to know a few little peculiarities 
in the play of nearly all the party. On this occasion that 


C)6 


knowledge saved me a good bit of money. Among the 
others was one man who could not control the expression 
of his face sufficiently to conceal the fact of his having 
bettered his hand in the draw whenever he happened to do 
so. He did not start, or exclaim, or smile, or do any of 
those obvious things that are only to be expected of infants 
or expert bluffers on occasions, but there was a slight tight- 
ening of the muscles around the mouth that indicated to 
me that he felt the necessity of giving no indication. 

“ It happened that a jack-pot was opened by a player 
on my left. The next two laid down their hands, and this 
man who sat at my right came in without looking at more 
than two cards in his hand. He had a way of lifting the 
corners of his cards one at a time before picking up his 
hand, and I knew that his invariable rule was not to come 
in on anything less than a pair of Jacks. It was therefore 
clear to me, as he doubtless intended it to be, that his first 
two cards were Jacks or better. 

“ It was my play next, and as I had four nines pat, I 
raised it the limit, keeping my eye on the man with the 
Jacks, more from habit than because of any feeling that 
it was necessary to do so. As he lifted his third card I saw 
him give a little start which told me that he had found a 
third. If it had been his fourth or fifth card that had oc- 
casioned the start, it might have been two pairs that he 
had found, but as it was the third I was morally certain 
that he had three Jacks at the very least and I looked with 
great equanimity to see him raise when he came his turn 
to bet again. If he had done so, I would, of course, have 
recognized my duty under the circumstances, and would 
have given him the limit again to think about. But he 
did not raise, and as the opener had simply made good, 
and there were only three of us in, of course I could 
not play my fours any harder just then. 


97 


“ In the draw the opener took one card, having two 
small pairs to draw to. My antagonist took two, and as 
he picked the first one up, I saw the lines about his mouth 
tighten in the way I have described, whereupon the beauty 
vanished from my four nines like a morning mist. I knew 
I was beaten, and although I took one card it was a mere 
matter of conventionality, and when I called his raise, the 
opener having bet a white chip and he having raised the 
limit, as I knew he would, I called the bet purely out of 
deference to the character of my own hand, feeling certain 
that his was the better. I would no more have raised him 
than I would have thrown my chips out of the window. 

“ There were two or three men looking over my shoul- 
ders and when they saw what I had done they fairly howled 
with amazement. One suggested that I ought to be sent 
to Sunday-school and another said that furniture should 
be broken over my body, but if they were astonished and 
grieved at first they were simply stunned when the other 
man showed his four Kings. It took me ten minutes to ex- 
plain why I had done what I did, and even after that I 
imagine that some of them thought I was a drooling infant 
who had been struck by luck as by lightning.” 

The story is a good one and despite the reputation of 
the narrator as a person of agile imagination and fluent 
speech it may be true. Certainly there is nothing inher- 
ently improbable in it, and if it be true it simply shows 
that he had mastered the A B C of the poker-player’s art. 
The only notable point in the yarn is the assertion that 
he quit play on the first bet. Most players would have 
been sufficiently dazzled by four nines pat to go back with 
at least one raise as a test of the correctness of their intui- 
tion. The play, as the Yale man made it, is only to be 
considered sound when the absolute correctness of his ob- 
servation and analysis is conceded. Having entire confi- 


9 8 


dence in that, as he had, the only criticism to be made on 
his play is that he ought not to have called, but should 
have thrown his hand down. Had he done that, however, 
he would not have seen the four Kings, and would have 
been haunted forever after by a lingering doubt as to 
whether or not he had been mistaken. 

The simple watching of another man’s tricks of physical 
expression of emotion, however, is elementary skill. One 
of the first things experience teaches is the necessity of 
overcoming those tricks in one’s own play so as to avoid 
the certainty of betraying the character of the hands held 
to every close observer around the table. It is perfectly 
true that many players, perhaps the majority, never suc- 
ceed in mastering themselves so thoroughly that they give 
no indication by facial expression, attitude or motion of 
the hand, of the value of the cards they hold, but on the 
other hand there are many players, perhaps also a major- 
ity, who never learn to read such signs in other players 
with any degree of accuracy unless they are very pro- 
nounced. The best players can do both, and they are the 
ones who possess an advantage that sometimes seems to 
amount to clairvoyance, over more impulsive and less 
guarded individuals. 

There is still a more scientific method of studying the 
play of an opponent which, if thoroughly mastered, would 
give any player an advantage in the game amounting to 
cards and spades in cassino. It may be assumed that a good 
player will speedily learn any of the nervous physical habits 
of his antagonists that have been referred to and will take 
all the advantage possible of any such betrayal of his hand 
that any other player may make. It remains true, however, 
that the opponent most to be feared is the one who has 
mastered himself in this respect, or who is gifted by nature 
with an impassive or expressionless face, and who has 


99 


nerves that are too steady to manifest emotion involun- 
tarily. The only thing to do with an antagonist of this 
description is to study his system of play, for it must never 
be forgotten for a moment that in poker a man plays not 
merely his own hand to win, but the unknown cards in the 
other man's hand to lose, and some judgment of the un- 
known hand must be formed before any sound bet can be 
made. 

Every man who plays poker plays on some system of 
his own. It may be that the system is not original with 
himself, and it may be the same system followed by thou- 
sands of other players, or it may be totally unlike any other 
man’s system, so far as he himself knows. It may be a 
strict adherence to certain well-known rules that are sup- 
posed to govern conservative play, or it may embrace such 
foolhardy stunts as drawing to three Flushes, intermediate 
Straights, a single Ace, or a King and nine, on the super- 
stition that these two cards, if of the same suit, are lucky. 
It may even be a system of constantly varying the style 
of play in order to mislead the other players, but such as 
it is, every player is tolerably certain to have some sort 
of system of playing his hands, which he will, as a general 
thing, adhere to with more or less fidelity. Whatever it 
may be, any other astute player who watches his play per- 
sistently and carefully can usually come pretty near finding 
out what it is in the course of time. And this system, 
whatever it may be, forms a part of the personality of the 
player. 

But, on the other hand, there are very few players who 
do not vary their systems at times. Even the most cautious 
and conservative player is likely to play more or less boldly 
when his luck is unusually good. And in various other 
contingencies it is to be expected that any player will dis- 
regard the rules which he has laid down as the best, gen- 
ii. oFC. 


IOO 


erally speaking. Good luck will change some men's play, 
and bad luck will change that of other men. This depends 
largely on the temperament of the individual and is also 
a part of his personality. 

Since the personality of every man is an exceedingly 
complicated proposition, and since it is of the utmost im- 
portance to every poker player to be able to judge the man 
behind the cards he is playing against, as well as to guess 
at the value of the cards, the study of individual character 
is a necessary part of the game. To illustrate : The first 
indication any player can have of the value of the cards 
held by an opponent is that afforded by the betting before 
the draw, unless, indeed, his opponent has betrayed him- 
self by some physical sign, it may be a look, or the contrac- 
tion merely of an eyelid, or it may be some more pro- 
nounced sign, like a start of surprise. So far as the scien- 
tific game goes the betting is the first. If the next man 
to the age comes in we have to consider whether he is a 
careful or a bold player. If he is generally careful it may 
be assumed that he has at least one pair, yet there is no 
certainty about this. If he has been having unusually good 
luck he may intend drawing to an Ace, or even taking 
five cards. On the other hand, if his luck be very bad he 
may have become desperate and have put up his ante en- 
tirely on the chances of the draw. We are obliged to take 
his personality into consideration. 

The next indication may come in the shape of a raise 
before the draw, and again we must study personality. 
The raise may mean a Four Flush, or it may mean nothing 
less than Three of a Kind, or it may be a bluff, pure and 
simple. By knowing the character of the player and his 
habits of play we may form a judgment as to what he 
holds; but what would be almost positive knowledge in 
the case of one player will be only a hazardous guess in 


IOI 


another case. And only in accordance with the judgment 
thus formed can we decide whether the cards we hold are 
worth the risk of seeing the raise. 

After the pot is closed and the draw is in order there 
comes the next opportunity to judge of what the other man 
holds before the draw. This is in watching the number of 
cards he takes, but again we find that we have to take 
into consideration the personality of the player, or at least 
the system he usually follows. If he takes three cards, 
of course the chances are that he has a pair, though it is 
no unusual thing for a reckless player to draw to an Ace 
and hold up some other card merely for the sake of con- 
veying the impression that he has a pair. We may suspect 
this from our knowledge of his play, but we will certainly 
assume for safety’s sake that he has a pair. We may 
change this opinion later if circumstances indicate that he 
is bluffing wildly, but it would be an extreme case which 
would lead to the supposition that a man drawing three 
cards for which he has had to pay does so on anything 
less than the strength of one pair. And we must, if we 
know him to be a cautious player, assume that he has a 
pair of a certain size or better. What that size may be 
again depends on his system and on the chance that for 
some reason or other he has varied his rule at this particular 
time. 

If he has drawn two cards only, the indication is not 
so clear. If he be one kind of player he will almost cer- 
tainly have Three of a Kind. If of another kind he may 
have a pair of Aces and be holding up a kicker merely as 
a bluff. Other players would be thought to have a pair 
only and an Ace which they would hold up in the hope of 
getting another Ace. Others still might be drawing to a 
Three Flush or even a Three Straight, and yet another class 
would certainly draw two cards if they held three parts of 
a Straight Flush. 


102 


In the case of a one-card draw the indication is still 
slighter. A player may draw to two pairs or a Four Flush 
or Four Straight or even an intermediate Straight, or he 
may on the other hand hold Three, or even Four of a Kind 
and draw a single card only in order to disguise the strength 
of his hand. The possibilities range from “ Busted 
Straight ” to a Royal Flush, and these possibilities can 
hardly be estimated by the personality of the player ex- 
cepting that we may assume that certain persons will not 
pay to draw to an intermediate Straight. 

At the completion of the draw, therefore, we find that 
we have been able to form at least a conjectural judgment 
of the various hands against which we are to compete for 
the possession of the pot. Even if some player has stood 
pat we are aided by our knowledge of his personality in 
deciding whether he really has a pat hand or is bluffing 
on two pairs or less — even on nothing at all. The bet- 
ting, however, after the draw will afford still further oppor- 
tunities for studying the character of our opponent and of 
profiting by what we already know of his general system 
of play. We inquire first whether he is one who is likely 
to bluff, remembering that any player is liable to bluff at 
times, but that some do it very rarely and only when their 
position relative to the age is likely to make a bluff effect- 
ive. If he be an habitual bluffer we feel safe in calling 
him, provided all the others have dropped out and we have 
a fairly good hand. If he merely trails along after some 
other player there is little opportunity to do more than 
calculate the mathematical probability of our hand being 
better than his, but even then we may judge something 
by the manner in which he pushes his chips forward or 
announces his bet. 

When it is remembered that in order to play poker with 
any degree of success one ought to be able to judge not 


103 


of the personality of one other player alone, but that of 
four or five or six, and to estimate the probabilities as 
indicated by each one and all of them, the almost infinite 
complexity of the game becomes at once apparent. With- 
out this study of personality, however, poker would be 
reduced to the level of a show-down. It would still, by 
reason of the variety of hands, be a game that might 
fascinate some persons, but it could be called intellectual 
no more than could the throwing of dice. 


104 


Betting Before the Draw. 

D RAW Poker is frequently called the game of con- 
tradictions, and the aptness of the description is 
shown clearly enough in many ways by a study of 
the effect of different manoeuvres in the game as they may 
be made under different circumstances. None, however, 
lends itself more readily to the purpose of illustration than 
the raise, especially when it is made before the draw. 
According to the condition of the game, and more em- 
phatically according to the position of the player who makes 
the raise, it may indicate either strength or comparative 
weakness in his cards, and it may serve either to swell the 
amount of money in the pot or to keep it from being in- 
creased. It is therefore evident that raising before the 
draw, even when it is done with discretion, may prove as 
disastrous in its results as a clumsily thrown boomerang 
and do more injury to the player who essays it than to his 
adversaries. It is not the only feature of the game, to be 
sure, that displays this characteristic, for any unsuccessful 
play, no matter how well conceived or how boldly made, 
is liable to react in the same way at times, but the raise 
before the draw presents points of considerable intricacy 
which should be carefully studied and well understood be- 
fore the play is ventured on. 

According to the position he occupies with reference 
to the age, a player may raise before the draw either for 
the purpose of frightening out as many other players as 
possible or with the desire to make the pot as large as he 
can. The first play would be made because of a lack of 
confidence in the chances he would have of improving his 


hand in the draw, while the latter would be inspired by 
his full confidence that no other hand at the table would 
equal his own. Either object may be attained by the raise 
if made in the proper position, and either one is liable to 
be missed if the player fails to take into consideration the 
number of other players who have already bet and the 
number who are yet to hear from. 

An analysis of some hands actually played will make 
this clear more readily than any theoretical statement is 
likely to do. Seven playing and A having the age, C has 
a pat Flush, ace high. Having confidence, which is fully 
justified, in the probability of this being a winning hand, 
he desires, as a matter of course, to make the pot as large 
as possible before the draw, since the fact of his standing 
pat and betting freely after the draw will probably keep 
the others out and so decrease the amount of his probable 
winnings on the hand. As it is his second say, however, 
he has to consider that there are five players to hear from 
after he bets and that no one of them is likely to see his raise 
unless he holds a reasonably strong hand without the draw. 
C therefore contents himself with merely coming in and 
looks for some other player to raise when his say comes. 

D comes in with a pair of Kings. E, having nothing 
to draw to, throws his hand in the discard. F, with three 
Queens, believes he has a good chance of winning, and 
raises $i. Had he sat where C does this would have been 
poor play, for the same reason that operated to prevent 
C from raising. Sitting where he does, however, there is 
nothing to criticise, for three men are already in, so that 
there is a certainty of a pot worth playing for, even though 
some of the others may decline to play against the pre- 
sumption of strong cards in his hand. G lays down, hav- 
ing only a pair of eights. A has a pair of Aces and, figur- 
ing the percentage of the bet, considers his chances worth 


io6 


playing for, even against a raise, so he comes in, making 
his ante good and putting up also the dollar called for by 
F’s raise. B had come in originally on a pair of nines, 
but he does not consider them strong enough to play 
against F, who has raised, A, who has seen the raise, and 
C, yet to hear from. He therefore resigns. 

C has now to consider entirely a different situation 
from the original one. He has only three players against 
him, and he has heard from each of them. Concerning D, 
he cannot judge with any accuracy, for D simply came in 
on his first say, so that he may have a single pair, or he may 
have been hoping for another player to raise, as C himself 
was hoping. As to the others, however, C can judge fairly 
well. F, by raising, undoubtedly indicated a strong hand, 
since he would not be likely to attempt a bluff sitting where 
he did. The only question is how strong the hand may be. 
It might be as low as a pair of Aces, for a great many 
players with more confidence than judgment esteem two 
Aces a strong enough hand before the draw to justify a 
raise. It would not in all probability be less than Aces, 
and might, of course, be anything at all better than that. 
C believes, however, that his Ace Flush is better than what 
F probably holds. And of A he has no fear, although A 
has seen the raise. 

The time has now come, therefore, when C can push 
the advantage he believes himself to have. It is unques- 
tionably his play to raise back. The question remains, 
however, as to how much it would be well to raise, the 
game being for table stakes, but a small one, no one having 
shown more than $10. To raise $i would very probably 
bring all three players in, and so increase the probable 
winnings, on which C is figuring, by $3 ; but on the other 
hand, a larger raise would not be likely to scare F out, 
and the possibility remains that both A and D, having 


shown strength enough to play, would remain even after a 
second raise. C therefore raises it $5. It is a good play, 
even though an Ace Flush can easily be beaten. According 
to the percentage of chances, however, it is a much stronger 
hand than is likely to be out against it, and C is playing it 
for what it is worth. 

The result justifies the play, which would have been 
sound in any case. D drops out. He reasons that a pair 
of Kings is not strong enough to induce him to see two 
raises. F no longer feels any great confidence in his three 
Queens, but recognizes that he has a fighting chance, since 
he may draw another Queen or a pair, so he makes good. 
A studies not only the chances of the draw, which are fairly 
good, but also the percentage of the bet he is called on to 
make. Five dollars on a pair of Aces in a game of this 
size is a heavy bet, but there is $14 already in the pot, 
the ante having been 10 cents, calling a quarter. As he 
gets fourteen to five, therefore, with no further raise pos- 
sible, he considers it a fair bet, and he comes in. 

This play is open to question. The odds of less than 
three to one in the betting are much less than the probable 
odds against A's winning, for, although there are only 
two hands against his Aces, the possibility is that each 
one of them is stronger than Aces. Of course, the fact 
that they are stronger really, cannot be taken into ac- 
count, because A cannot know that they are, but his knowl- 
edge of poker should be sufficient to enable him to judge 
that they are, and his judgment should be sound enough 
to prevent him from betting against stronger hands be- 
fore the draw, unless the odds in his favor in the betting 
were equal to the odds against him in the draw. He has 
been playing in good luck, however, and determines to 
back the luck. To how great an extent a player is justi- 
fied in doing this, is something that cannot be determined 


io8 


by any rule of percentage or any principles of poker that 
can be formulated. When the acknowledgment is once 
made, that luck is a factor in the game, no man can fig- 
ure with any precision on the weight it will have in any 
given problem, and there is no possibility of denying that 
chances do run, at times, in favor of or against particular 
players in a way that can only be explained by the theory 
of luck. It is true, too, that the most strictly scientific 
poker playing is often beaten by pure luck, so that he 
would be a dogmatic theorist who should deny the wisdom 
of backing one’s luck on occasions. 

On this particular occasion it seemed almost as if A’s 
luck was well worth backing, for he caught a third Ace, 
C having stood pat, as he was compelled to do, and F 
having drawn two cards without bettering his hand. A’s 
hand was therefore, he considered, probably good against 
F, the latter having presumably drawn to three of a kind, 
and A’s three Aces being the best of any three in the 
deck. C, to be sure, had stood pat, but that he would 
be very likely to do if he had raised it on two large pairs, 
and A considered with reason that his three Aces were 
worth a call on a single bet. 

It will be seen that the pot was now surely C’s prop- 
erty unless he should be bluffed out, and that was not a 
contingency likely to arise, as no good player would lay 
down an Ace Flush before a two-card or a three-card draw 
under ordinary circumstances. At the worst he could call. 
C, however, sat now in the worst place he could have for 
a bet, as it was his first say. If he should bet too heavily 
he would be likely to get only one call or none at all, 
while if he bet too little he would miss the winnings he 
might make. He could not expect a raise from either of 
the other players excepting under the wholly undesirable 
condition of one of them having made a Full or a Four 


( 


109 

of a Kind, so his only hope was to make his bet as large 
as he thought they would be likely to call. In decid- 
ing this point, he took into consideration the fact that the 
pot now contained $19 — a sum which neither player would 
be willing to see him take without a call. His judgment 
was that $5 was about the sum to venture, and accord- 
ingly he bet that. F called, on the chance that C might 
be bluffing, and on the further chance that A might not 
have bettered his pair in the draw, or that, if he had bet- 
tered, he had not made better than three Queens. A called, 
also on the chance that C was bluffing and on the theory 
that his own threes were better than any three that F could 
have. C therefore won $34 in the pot, of which he had 
himself contributed $11.25, making his gains $22.75. 

It will be noticed that in the playing of this hand C 
sat in a poor place on the first round, but that after F 
had raised, C’s place was almost the best for the purpose 
of a second raise, and that after the draw it was again 
a poor place for him to have. A different deal, that would 
have given C the age, would have entirely changed the 
play, provided that all the players had shown equal judg- 
ment, and might have produced a different result. To 
illustrate this it is worth while to analyze the playing of 
another deal, very similar to this, out of the great number 
of which the author has made a record. The hands were 
not exactly the same. That would be remarkable indeed, 
but they were nearly like those described and were held 
in similar order, G having the age, and having put up the 
same ten-cent blind, calling a quarter. A, having first say 
and holding Aces and Tens before the draw, came in with- 
out raising. B also came in, having two Queens. C 
held three Jacks, and with a view to keeping some of the 
others out, his hand being one that might easily be 
beaten in the draw, raised it $2. D, having nothing, 


dropped out. E had eights up and saw the raise. F, 
having three sevens, was also anxious to make the circle 
narrower, and he raised it again $2. This gave an excel- 
lent opportunity to G, who held a King Flush, to push the 
betting along. His hand would have justified a larger 
raise than he made, but he figured that he might get still 
another raise before the draw, and that if he should not, 
there would still be betting after the draw, three hands 
being almost certainly strong, and one yet to hear from on 
the first raise. H therefore saw C and F and put up $3 
more. 

A had then to consider whether Aces and Tens were 
worth betting $7 on when there was $16.50 in the pot 
already. He decided that they were, because B, C, E and 
F were yet to hear from and the odds were likely to be 
still larger in his favor provided he should fill, as he had 
a reasonable chance of doing. B, however, saw no use in 
playing a pair of Queens against the game as it stood, 
and he threw his cards on the table. C, E and F made 
good, none of them feeling himself strong enough to raise 
again. There were therefore $22.25 m ^ ie P ot before the 
draw. 

In the draw each drew to the strength of his hand. 
A might very possibly have stood pat on his Aces up as 
a bluff, had it not been that G, having first call, stood pat, 
and A decided that it would be too difficult to bluff against 
a pat hand. It happened that no one bettered, and G, hav- 
ing the strongest hand and also having the age, might 
be expected to be able to force the playing. His standing 
pat, however, had inspired the others with caution, and A 
bet only a white chip. None of the others raised until it 
came to G, when he raised it $5. This gave A one chance 
to bluff on his two pairs and he did so, though the play 
was not a good one, since a one-card draw is tolerably 


certain to be called if there is anything of value out against 
it. A raised it $5, however, on a venture, and C trailed 
along. G had then to decide whether to call A or to raise 
again. There was a probability that A might have filled 
either a Flush or a Full. If it were a Flush G’s hand 
would be worth another raise; if A had a Full, it would be 
worth nothing. So he decided, correctly, to call. 

In this hand the pot was swelled to $52.50 and was 
won, as the other was, by a High Flush, but the winner 
did not really press his advantage as hard as C did in the 
first hand described, though he got considerably more 
profit. The difference lay almost altogether in the matter 
of position, for there was only one play made outside of 
A’s bluff that was open to criticism. That was C’s last 
play. He put up $10 against the $37.50 already in the 
pot, when the chances were greatly in excess of those odds 
that he could not win. It was poor play and showed that 
C had much to learn regarding the wisdom of laying down 
even strong cards when the chances are against them. Oc- 
casionally a pot may be lost by doing it, but much money 
is saved by it in the long run. 

Enough has been said in the analysis of the play in 
two deals to indicate the advantage of the position to one 
who is attempting to bluff. It would not be too strong, 
perhaps, to say that it indicates the folly of undertaking 
to bluff if one sits in a poor position. A bluff is often, 
of course, the result of the inspiration of the moment and 
is born of a conviction that the other man lacks confidence 
in his hand even if it be a reasonably strong one, but 
perhaps still oftener it is a deliberately planned movement 
in which advantage is taken of every favoring circumstance 
to impress one’s adversaries with the strength of one’s 
hand, regardless of what the hand contains. 

To obtain the greatest effect in this series of manoeuvres, 


supposing the bluff to be deliberately planned, it is highly 
advisable to begin before the draw, and a judicious raise 
at that stage of the play will often create an impression 
that may be strengthened two or three times afterward, 
regardless of whatever skill the bluffer may have as an 
actor, while that skill may also, of course, serve as a great 
help in the bluff. 

This raise before the draw, if it be done to create a 
fictitious appearance, is seldom attempted if any other 
player has shown signs of strength, nor is it usually, con- 
sidered good play unless all or nearly all the other players 
have been heard from. If the would-be bluffer holds the 
age, he is of course placed to the best advantage, but if 
he be the dealer, sitting next before the age, with six or 
seven playing, the position is a good one. 

The next advantage of this position comes in the draw. 
Of course, the dealer serves himself last, thus knowing 
what each other player takes before being compelled even 
to decide what he will take for himself. If, then, he has 
made a bluffing bet on a single pair and everybody else 
has drawn three, he may conclude to take two, in order to 
give the impression that he has three of a kind, or even 
to draw one, to set his opponents guessing as to whether 
he is drawing to two pairs or a four-straight or a four- 
flush. Or he may decide to stand pat, which, together 
with the raise before the draw, is a strong bluff. After 
this, of course, the opportunities of the betting after the 
draw remain, and the bluff may again be strengthened. 
Not one of these three chances, it will be observed, is avail- 
able to the first, second or third player after the age in 
anything like the same degree that they are to the fifth or 
sixth man after the age. It remains true, however, that a 
bluff made almost under any circumstances is the stronger 
if it be begun with a bet before the draw. 


As to Laying Down. 



LL problems in poker — and their name is legion — 
are finally resolved into one crucial question, 
“ Shall we bet or lay down? ” It must always be 
remembered that up to the moment of the call or the sur- 
render which decides the ownership of the pot each feature 
of the play is in anticipation of some further development. 
Whatever is done before the draw is done tentatively. The 
player either has enough in his hand to justify the risk 
of his chips or he believes that he has a chance of better- 
ing his hand and that this chance is good enough, consid- 
ering the amount in the pot, to justify a bet at the per- 
centage offered. And after the draw no bettor, excepting 
the player who has the last say, can know whether the 
bet he puts up will be all he will be called to venture to 
protect his chance for the pot. 

This privilege of the last say is always liable to be 
transferred from one player to another by a raise. Be- 
fore the draw, and on the first round of bets after the draw, 
provided no one raises, it belongs to the age, or to the 
player on the dealer’s left, an arbitrary arrangement neces- 
sary in order to preserve the due order of betting, but 
though, according to the rules, the age never passes, its 
value disappears the moment a raise is made by any player 
excepting the first one to the left of the age. It remains 
true, therefore, that the final say can only be had by the 
last player who remains in, after all the others, excepting 
the man who raised, have had the opportunity to play or 
lay down. 


It is only the man who has this last say, therefore, 
who can know whether his bet is the final one. If there 
remains with any one the privilege of raising, all the others 
who desire to remain in must see the raise in order to do 
so. Obviously no man can know positively whether he is 
going to win or lose if he bets, and on his judgment in 
answering this grand question whenever the play comes 
to him depends his success in poker. If he holds a Royal 
Flush he may know that he cannot lose, but he cannot 
know that he will win, since there may be a Royal Flush 
out against him. 

It is equally obvious that no positive rule can be laid 
down by which a man can determine positively whether any 
bet will win. If it were possible to do this, poker would no 
longer be a game of chance, or, in fact, a game in any sense 
of the word. It is entirely possible, however, to analyze 
the playing of a few sample hands, and form an opinion 
of the judgment shown by each player, thus arriving at 
certain general rules of value in actual play. 

The following hands, held in actual play by a party 
of seven, will serve as an example, and the way they were 
played was not only interesting, but instructive. Before 
the draw, A, who held the age, had two pairs, Aces and 
Tens. B held a pair of Queens, C a Four Flush of dia- 
monds, nine, seven, four and three; D Queen High, E 
three fours, F a pair of sixes and G a pair of Jacks. 

The ante was io cents, calling a quarter. B came in, 
holding his Queens to be well worth a bet considering the 
possibilities of the draw. C also came in. Had he held 
the age, no raise being made before it came to him, he 
would have raised on the theory that he had nine chances 
in forty-seven of making a tolerably strong hand, and, 
moreover, that the raise would be likely to force some of 
his competitors out, thereby decreasing the chances of his 


Flush being beaten in case he should get it. Sitting 
where he did, however, he considered the chance of some 
one else making the raise to be fairly good, and his pos- 
sible hand strong enough to play against any single raise, 
even with all seven players in. This theory of play would 
not be followed, however, by all good players. It would 
be equally defensible for him to have raised, since some 
of the five players yet to hear from would be likely to 
drop out if he raised, and the Flush he would hold, even 
by filling, would hardly be strong enough for him to de- 
sire too much competition. The play would be sound either 
way. 

D having no pair and no prospect of a Straight or a 
Flush, passed out, as any player of even moderate caution 
would do. E raised it the limit, which was 50 cents, 
entirely for the purpose of driving the others out. His 
hand before the draw was undoubtedly strong, but the 
chance of its being beaten in the draw, if all should stay 
in, was fully equal to his chance of bettering, which he 
could only do by drawing a fourth four or a pair of some 
other denomination. 

F, having only a pair of sixes to draw to, had either to 
relinquish his hand or to put up 75 cents to play, when 
there was only $1.35 in the pot, with two players yet 
to hear from and two more who might possibly raise back 
when it came their turn to make good. Instead of drop- 
ping out, as ordinary caution would have dictated, how- 
ever, he put up his 75 cents. Of course he had a fair 
chance of making three sixes, a remote chance of mak- 
ing a Full House in the draw, and a still more re- 
mote chance of making four sixes. As opposed to 
these chances there was a moral certainty that the three 
players already in had at least as good cards, and probably 
better than he held, while E had almost certainly a strong 


ii 6 


hand. If there had been a large sum already in the pot, 
the play might have been justified by the percentage of 
the bet, but as it was it was reckless in the extreme. 

G, playing a more cautious game, dropped his two Jacks. 
He would undoubtedly have come in if it had not been 
for E’s raise, since he had a fair chance of making three 
Jacks, which would have been a strong enough hand to 
play. His passing out, however, was better play than it 
would have been to put up 75 cents against four 
hands already in, one of which (E) was presumably a 
strong one, another of which (F) was probably as good 
or better than his own and the other two probably as good. 
Moreover, there was only $2.10 in the pot, so that he 
would have got less than three to one odds, and there were 
still three chances remaining that he would be obliged to 
put up more money before the preliminary betting would 
end. 

A, having Aces up, came in. In the first place, it cost 
him only 65 cents against the $2.10 in the pot, so that 
his odds were better than G’s (for the amount of his ante 
is not to be reckoned as a part of his bet, since that was 
already gone), and, secondly, he held a moderately strong 
hand, with four chances in forty-seven of making a very 
strong one. This hand is considered by many players 
strong enough to justify a second raise, but B and C were 
yet to hear from on the original raise and there remained 
the possibility that either one or both of them would raise. 
A’s play, therefore, in simply making good was unques- 
tionably sound. 

It remained for B and C to come in on E’s raise, but 
B, being a conservative player at all times, and having had 
poor luck for the preceding half hour, refused to play his 
single pair against a raise that had been seen by two other 
players. In this case run of luck is ordinarily held to be 


a justifiable factor in determining the play, and while his 
coming in, if he had decided to play, would not have been 
open to criticism, his passing out was equally good poker. 

C, on the other hand, having his Four Flush, put up 
his 50 cents unhesitatingly, and raised it again 50 cents. 
It will be observed that his position this time was alto- 
gether different from what it was when he came in orig- 
inally. Then he had five players to hear from with no 
means of judging their hands. Moreover, there was only 
35 cents in the pot. Now, however, there was $2.73 in 
the pot, which he made $3.25 by seeing E’s raise. His 
own raise of 50 cents, therefore, was good poker, since he 
had only three antagonists and might hope to force one or 
possibly two of them out. He judged E’s hand to be strong, 
since he had made the first raise, but thought that F and 
A had come in hoping to better, but having only a pros- 
pect to play on. His judgment of the hands was accurate, 
as it happened, but his hope of forcing F and A to retire 
proved abortive. All three saw his raise and the draw was 
in order. 

It is to be noticed that up to this point the play has 
been correct with the exception of the way F had backed 
an almost worthless hand. He was certainly venturesome 
in putting up 75 cents in the first place on so long a chance 
as bettering sixes, but he made a further error, though a 
very common one, when he put up 50 cents more on the 
second raise. His argument was that, having bet the first 
time, he was warranted in betting more to protect what he 
had in already. This line of reasoning is frequently fol- 
lowed, though its fallacy is clear. His chance of winning 
was too small to justify any play, and although he got 
better odds in the second bet, there being $4.25 in the pot 
against the 50 cents he put in, the odds against his filling 
were even greater. 


1 18 


The draw changed the condition materially, as it fre- 
quently does, and by one of those chances that seem to 
discredit all rules of play, the only man who had played 
poor poker was the only man to better his hand. F drew 
a third six and two nines, making a Full House, while the 
other three, each drawing to the strength of his hand, got 
nothing of value. It being C’s first bet, he passed out. 
Three presumably strong hands were out against his Four 
Flush and it would have been hopeless for him to attempt 
to bluff. E bet the limit, hoping to impress the others 
with the strength of the Three of a Kind with which they 
credited him, seeing that he had drawn two cards. F, 
having now a Full, raised him the limit, whereupon A 
passed out. Aces up had no place in a struggle against 
Three of a Kind in one hand and a pair that had evidently 
been bettered in the other. Had he had only F to play 
against he would have called, for F would have bet even 
if he had only made a second pair, but the fact of F hav- 
ing raised E, who only drew two cards, was evidence that 
he had at least three big ones. Therefore A’s play was 
correct. 

It remained for E to decide whether to call or resign, 
either of which would have been justifiable, since his Three 
of a Kind was very small. He decided to call on the theory 
that F was possibly bluffing, and there was $6.75 in the 
pot. His further venture of 50 cents was therefore good 
play, though it lost, and the only man who had overplayed 
his hand, recklessly, won the money. As was said, cir- 
cumstances like these (and such things are common in 
poker) apparently discredit the rules which undoubtedly 
govern good play in the game. It is not to be called an 
extraordinary thing that a player should make a Full House 
drawing to a single pair, and a Full House is unquestion- 
ably a strong enough hand to justify backing heavily. It 


must not be forgotten, however, that although such a draw 
is occasionally made, the odds against it are very heavy. 

F, however, in paying for the chance of getting it, made 
two bets, in neither of which did he get odds approximat- 
ing to those against him in the draw. The first time he 
put up 75 cents against $1.35 that was in the pot, thus 
getting less than two to one. The second time he put up 
50 cents against $4.25 in the pot, getting seventeen to two. 
Even the latter was wholly out of proportion to the odds 
of the draw, and the man who continues to play in this 
fashion will eventually go broke, despite the occasional win- 
ning of a pot in the manner described. 

The foregoing deal, though it had a wholly fortuitous 
outcome, was by no means to be classed as a phenomenal 
one. It was hardly unusual enough to excite more than 
a passing remark, and has been described in detail 
here merely for the purpose of analyzing the play and 
showing how correct poker is always liable to be beaten 
by a fluke. A deal that occurred in the same sitting only 
a few minutes later, however, was remarkable enough to 
warrant description for the sake of showing how good 
play will win against good cards. 

The deal was again with G, giving A the age. The 
ante was the same, A having put up 10 cents for a quar- 
ter. In the deal A got the seven, eight, nine and ten of 
diamonds; B three sixes, C Kings and nines, D a pair of 
Aces, E ten high, F a pair of Jacks and G the Queen, nine, 
seven and six of hearts. B put up his quarter, C came 
in, D followed, E passed, F came in and G did likewise. 
A, having a chance for a Straight Flush, a Flush or a 
Straight, raised it the limit. B, C, D and G stayed, F 
dropping out. 

The play thus far was above criticism. G might have 
raised on the strength of his Four Flush, as A was the only 


120 


remaining player to hear from, but the wisdom of such a 
raise is open to dispute, and no criticism is due. A, on 
the other hand, had only a Four Flush, but his chance was 
much better, and if he should happen to catch the Straight 
Flush he would want as large a pot as possible to play for, 
so his raise was unquestionably good play. F had a fair 
chance only and was justified in passing, while the others 
were equally justified in staying. 

In the draw A caught the Jack of clubs, making a 
Straight, Jack high. B and C failed to better, D got a 
third Ace and G drew a spade. B bet the limit, C stayed, 
D raised, making it a dollar to play, and G passed. A 
raised again, and B stayed, still having confidence enough 
in his three sixes to make him call. C passed and D raised 
it again. 

This play raises a question. Only three players were 
left in, and A had drawn only one card, while B had drawn 
two. D had no fear of B, since his own three would beat 
those to which B had probably drawn, and as threes are 
hard to better in the draw, it was probable that B had not 
bettered. The real struggle was therefore between A and 
D, and D, realizing this, saw his opportunity for a bold 
play. He sat in the right place for it, since, even if A should 
raise back again, he could make a show of strength by still 
another raise, and so possibly force A to resign in case he 
was bluffing or had filled only a small Straight. As was 
said, D made the play. 

A had then to judge of the two hands against him. 
He estimated B’s hand correctly as Three of a Kind, and 
consequently had no fear of him. D, however, had drawn 
three cards, so his hand was problematical. The chances 
were that he had only Three of a Kind, but on the other 
hand he had not only seen A’s raise after A had drawn 
one, but he had raised back, indicating either a bluff or a 


I 2 1 


strong hand. A’s own hand was not very strong, but he 
decided, in order to test D still further, to raise again, 
which he did, and B passed out. 

D then had to consider whether A had filled or was 
bluffing, either of which was possible. He knew, however, 
that A seldom bluffed, and he decided that he had prob- 
ably filled. In that case, of course, D’s hand was worth- 
less, and his only chance of winning the pot was by making 
A believe that he held a stronger hand than he really had. 
A call would have been counted perfectly sound play, on 
the theory that A might not have filled, and that there was 
enough in the pot to justify paying 50 cents to see. For 
there was in fact $10.50 on the table. 

D decided, however, not to call. There remained a 
chance that A had filled a small Straight, in which case 
a call would give him the pot, but if D should raise there 
was a possibility that A would believe himself beaten and 
would lay down his cards, reasoning that D would scarcely 
go so far as to raise three times unless he had something 
better than Three of a Kind. It was not a promising 
chance, but D decided to risk a dollar on it against the 
$10.50, and he accordingly raised again. 

A had now to decide whether to throw down his cards, 
to call or to raise again. It was a test of nerve, for he had 
to judge D’s play either as a bluff or as evidence of a strong 
hand, stronger in all probability than A’s. He might have 
Three of a Kind, or a Full House, or Fours. In the first 

case A would win, but against either of the others he would 

♦ 

lose. It would certainly have been sound play to call, but 
D had succeeded in doing what he had undertaken to do 
by his successive raises, namely, to convince A that he had 
a strong hand, and A, losing his courage, lost his nerve 
entirely and threw down his cards. It was indubitable 
proof of the superiority of D’s play, for although D sat 


122 


in a good position for a bluff as the play ran, A had also a 
good position and should have played his hand, at least to 
the extent of a call. 

It may be argued that it was A’s error rather than D’s 
good play that gave the latter the pot, but A would have 
made no such error had it not been for the consummate 
judgment and excellent nerve which enabled D to see his 
opportunity and press his play sufficiently to overawe A. 
The hand was one which illustrates very well the way in 
which a good player can deceive a poorer one as to the 
value of his cards and so win against a stronger competitor. 

It shows, too, the great advantage that may lie in posi- 
tion. Had D sat where B did and been obliged to bet first, 
C would have come in as he did after B’s bet, and B, sit- 
ting in D’s place with three fours, would very probably 
have raised, though possibly he would not with two one- 
card draws to hear from. Had he raised, however, A would 
have raised again, as he did, and D would then have had 
two raises to see before he could himself raise. It would 
have left him in doubt as to all three hands, for C had not 
at that time dropped out, and the prospect of a successful 
bluff would not have been as good. For it is certain that 
D’s actual play was of the nature of a bluff, though there 
was all the time the possibility that his cards were the best, 
and it was not, therefore, a pure bluff. 

Had it been purely a bluff the advantage of the posi- 
tion would have been equally great, and unless he had be- 
trayed his weakness by his manner he would have won 
on the same play even though he had not bettered his orig- 
inal pair. The chance of the bluff, it is easily to be seen, 
depends largely on position, and though bluffing may be 
successful even when poorly done, the inexperienced player 
will do well to avoid trying it until he shall have studied 
the sequence of the betting. 


123 


Playing a Strong Hand. 

T HE experienced player who holds a strong hand in 
the game of Draw Poker is by no means satisfied 
when he captures the pot, if he looks back over his 
play and sees that by more skilful manoeuvring he might 
have made more. The mere winning of a hand, gratify- 
ing as it is, may be accomplished by any beginner who 
holds good cards. It is no test of skill and no fair illus- 
tration of the possibilities of the game, for in every case 
the show-down does the final work, providing there is a 
call, and a Royal Flush is as efficacious in the hands of 
a tyro as in the hands of the best player living. But while 
it is equally as efficacious, it is not likely to be equally valu- 
able, since the beginner cannot hope to push his advan- 
tage as an old player would, especially if he sits in a posi- 
tion in which a raise is a clear indication of his strength. 

The advantages that come from a perfect nerve, and 
the power to conceal all emotion, are too well understood 
to need explanation. The man who shows elation, confi- 
dence or doubt in the expression of his countenance, or by 
any trick of action, is at the mercy of his opponents to a 
great extent, and no one can hope for much success at the 
game until he has learned to control his features, and to 
handle his cards in as nearly an automatic fashion as pos- 
sible. An instance of this was given by a fairly good player 
who was beaten all one winter by those who played with him 
in a friendly game. He was puzzled for a long time, and 
not until the other players in true friendly fashion told him 
of his habit, did he realize that he had been advertising 


124 


every good hand he had held. He had unconsciously 
formed the habit of laying his cards down in front of him, 
face down, of course, whenever they were sufficient to in- 
spire him with confidence, and handling his chips as he 
looked around to see what the others were doing. It was 
so simple and transparent a trick that he could hardly be- 
lieve, when he was first told, that he had been guilty of 
it, for he had schooled his features to impassibility and did 
not imagine that he showed his strength in any way ex- 
cepting by his betting. 

In this particular, however, it is impossible to lay down 
any rules, since the nervous player is tolerably sure to 
betray his hand in some fashion to those who are shrewd 
enough to read him. A story has been told of two superb 
players being pitted against each other when the stakes 
were extraordinarily heavy, and when one of the two had 
an unusually strong hand. The other was bluffing and had 
done it so skilfully that the man with the better hand was 
fairly puzzled. The bluffer had made a large raise, and 
the other hesitated in his play, fearing that he was beaten, 
but unwilling even to call with so good a hand as he held, 
and desirous of raising back. He looked long and intently 
at the bluffer, seeking to find some indication in his face 
by which his strength could be estimated, but the other's 
features told no story whatever, and he was about to call, 
when he saw a tiny drop of perspiration start out on the 
other's forehead. It was enough. The player who was really 
strong, without an instant of further pause, shoved for- 
ward twice the amount of the other's raise, and the bluffer 
threw down his cards. 

Such instances show how men of shrewd perception can 
learn to read the play of others, but no treatise can be writ- 
ten from which the art can be learned. There is, however, 
a vast field of study in the play itself, which can be mas- 


125 


tered by application, and which is as fertile in results as 
the mental skill which sometimes seems to approach clair- 
voyance. Without this technical knowledge, indeed, the 
clairvoyant power is crippled, and though it will produce 
results, the results will not be so considerable as they might. 

A deal played by six expert players in a New York 
club will illustrate this by showing how the holder of the 
strongest cards won more money by refusing several times 
to raise than he would probably have made had he played, 
as a novice would, to the strength of his hand. A was deal- 
ing, so that B had the age, and the ante was 50 cents, 
calling a dollar, the game being for table stakes. C dis- 
covered Queens and sevens, so he came in with $1. D 
had four tens pat, and had he sat in a different position 
would undoubtedly have raised the bet, but four men being 
yet to hear from, he contented himself with simply putting 
in his dollar. E, having Aces and Jacks, raised it $5. F, 
with three Kings, might be expected to raise it again, but 
he also was playing a waiting game, and feared the effect 
of a double raise on the other players. He therefore simply 
saw the raise. A, however, had an Ace Flush and he raised 
it $10. B, having nothing, relinquished his blind. 

Up to this point the only really notable thing about the 
deal was the unusual strength of the hands. Five reason- 
ably strong hands, two of them being very strong, are not 
often seen before the draw, but in this case they were out 
and the record was verified by all the players after the game 
was over. The play on this first round had been sound, 
but not remarkable. On the second round, however, there 
was some clever play. C felt that his show on Queens up 
was a dubious one, but the hope of a Queen Full carried 
him along, and he put up his $15, thinking that if the 
others all filled, he would have four to one in the betting, 
and a possible chance of winning. It was then D’s say, 


126 


and, had he raised, his play could not have been criticised, 
since he had secured two strong antagonists and might 
reasonably have expected a large pot. He reasoned, how- 
ever, that if he concealed his strength at that stage of the 
betting, there might be more raising, even without his aid, 
so he simply made good. It was close reasoning and clever 
play. 

E studied his hand and, with his possible chance of a 
Full, decided to raise again. It was over-playing his hand, 
but he had been playing in luck and had more confidence 
than was good for him. He put up $20, making a raise 
of $10 over A’s raise. F considered his chances on three 
Kings good enough for the money, and he made good again, 
but decided wisely that it was no place for him to raise. 
A continued to have confidence in his Ace Flush, and, to 
D’s great delight, he raised it ten more. C by this time had 
lost confidence in his Queens up, but remembering that 
there was $120.50 in the pot and that it only cost him $20 
to go in, he made good. 

It was up to D again, and there was a strong enough 
temptation to make an average player raise in turn, and, 
had he made the play, it would have been justified. He 
contented himself again, however, with merely seeing the 
bets that had been made, reasoning that he had the best 
position at the table as well as probably the best hand, there 
being a confident player on each side of him who would 
probably push the struggle, and remembering, furthermore, 
that he would have a chance in the draw to puzzle his op- 
ponents, and so probably increase his profits. E and F 
each made good and there was $180.50 in the pot before 
the draw. 

When cards were called for C took one and failed to 
better. D also took one and looked at it with ostentatious 
indifference, hoping to impress the other players with the 


127 


notion that he was drawing to a Straight or a Flush, and 
was afraid of betraying himself. E caught a third Jack 
in the draw, making a Full Hand, F failed to better his 
hand and A, of course, stood pat. 

The betting was then in order and C put up a white 
chip. D saw it and E raised it $10. F had only $3 left 
and he called for a show with that. A raised it $15 and 
C threw down his hand. It looked then as if D might not 
get another chance to raise, and that if he wanted to real- 
v ize on his four tens it was high time for him to do some- 
thing more than trail along. He had watched E closely, 
however, and felt sure that he had bettered his hand, in 
which case, having raised twice before the draw, he would 
be pretty certain to raise at least once more, so D merely 
saw the two raises. His judgment was correct and the long- 
est chance he had taken thus far turned in his favor, for 
E, with justifiable confidence in his Jack Full, raised it 
$25. A had now to consider that he had two one-card 
draws against him and that his Ace Flush might easily be 
outclassed. There remained, however, the chance that it 
might be good, and he saw the raise simply as a matter 
of percentage, there being $285.50 in the pot, against which 
he had only to put $25, with only one man to hear from, 
and he being one who had not yet raised. 

D’s last chance had now come, and the only question 
was how much of a raise the two others would stand. He 
decided that if he made a large bet, they would both think 
he was bluffing and that E might raise again, while A was 
likely to drop out even if D should only make a small raise 
and E should raise again. On this reasoning he pushed 
forward $75, being the amount of E’s raise, and $50 more. 

His play had been masterly throughout, and this last 
bet was as clever as anything he had done before, for, as 
he calculated, the presumption was strong that he was bluff- 


128 


ing. E retained his confidence in his Jack Full sufficiently 
to raise him $50, and A dropped out, saying, “ If it were 
a question of calling either one of you I’d do it.” 

D now having only one antagonist, and feeling sure that 
there was a Full Hand against his four tens, had one chance 
remaining. If he could induce E to continue to believe that 
he was bluffing he might get several bets more, so he raised 
it again $50. E, however, counting up his chips, found 
only about $70 in front of him, and not thinking it worth 
while to make a small raise, called. D therefore took in 
$635.50 on his hand, which was probably several times as 
much as he would have taken had he pushed the game at 
first. 

There is no better way of demonstrating a theory like 
this than by contrasting the play of one collection of hands 
with that of another, and noting the difference in the re- 
sult. With this in view the author has noted many hun- 
dreds of deals and kept memoranda of the way they have 
been played. The difference is amazing to those who play 
poker in the comfortable, happy-go-lucky theory that the 
best cards are sure to win in the long run, excepting in the 
case of an occasional bluff, and that the science of the bet- 
ting is a comparatively unimportant part of the game. 

To prove, therefore, the excellence of the play just de- 
scribed it is worth while to compare it with a very similar 
collection of hands, held on another occasion by another 
party of players. In this hand A, the dealer, held before 
the draw a Deuce Full on Jacks, pat. B, the age man, 
had a pair of Kings; C had three sevens; D had four 
Queens; E had eight, seven, six and five of clubs; and 
F a pair of Aces. 

It will be noticed that the commanding hand was in 
the same relative position to the draw as in the deal de- 
scribed above, while there was a general similarity also 


shown in the other hands, which, as was said, is the rea- 
son this particular deal was selected as a comparison. One 
striking difference exists, however, in that E, instead of 
having a chance for an Ace Full or a Jack Full, had a 
chance for either a Flush or a Straight, and a small chance 
for a Straight Flush. 

In the play before the draw, the ante being, as in the 
other case, 50 cents, calling a dollar, and the game for table 
stakes, C, who was first man to come in, put up his dollar. 
D with his fours raised it $5, thereby notifying the four 
men yet to hear from that he was either very strong or 
intending to bluff. The raise was of course justified by 
the strength of his hand, but it was decidedly ill-advised, 
since all the others were likely to stay out altogether and 
leave him with only $1.50 winnings to show for a remark- 
ably strong hand. 

As it happened, however, there were other strong hands 
out. E, being more prudent, declined to raise on the 
strength of his Four-Straight Flush, as he might have done 
if he had had better position, and merely put up his $6, 
waiting to see what the others would do. F, looking for 
a possible third Ace and, perhaps, even more in the draw, 
stayed, also without raising. A raised it $10, and B dropped 
out, believing that a single pair, even of Kings, had no place 
in a struggle against two raises. C, however, made good, 
believing that three sevens had a chance in the draw. 

D had now knowledge of only one strong opponent, 
and thinking that the others would probably drop out in 
case he should raise, he simply made good. This was 
doubtless good reasoning, but he had made his mistake al- 
ready, and E made good while F dropped out, not caring 
to push a single pair any further. 

There was then only $70.50 in the pot as against the 
$180.50 before the draw which D had secured in the former 


hand under almost precisely similar conditions, by lying low 
and letting the others do the struggling. It is likely, as 
will be seen by analysis, that if the holder of the four 
Oueens had been as shrewd as the holder of the four tens 
was he might have done equally well, for E would very 
probably have made a raise on his Four-Straight Flush if 
D had not, and A would undoubtedly have raised back, as 
he did, on his pat Full. This would even have afforded D 
an opportunity to raise again to better advantage had he 
chosen to do so when it came to him the second time to 
play. Having forced the play at the beginning, however, 
his moderation on the second round was justifiable if not 
particularly clever. He had forced out two players before 
the draw and only retained three antagonists by reason of 
the accident of their having strong hands, or at least, in 
the case of E, the chance for a tremendously strong one. 

In the draw C failed to better and D, instead of draw- 
ing one card, stood pat. This was a variation of the usual 
play of drawing one card to Four of a Kind, and it is only 
fair to say that he adopted the play he did with a view of 
misleading A, whom he considered his only antagonist. 
Believing that A had a pat hand, as in reality he had, D 
hoped that A would believe his own hand to be probably 
the stronger, and would so be encouraged to bet. The 
strategy was successful so far as A was concerned, but D 
forgot that he had also to impress E and C, and that they, 
who had not shown strength by raising, would be more 
likely to fear him standing pat than they would if he drew 
one card, thereby indicating the probability of his holding 
two pairs or an imperfect hand. 

The next to draw was E, who caught the ten of clubs, 
making a strong Flush, but not a Straight Flush. F and 
B were already out and A stood pat, as he was obliged to do. 

C, having first say, put up a white chip, and D, hav- 


ing seen that his previous raise was poor play, and being 
sure that A would raise, merely came in. This was doubt- 
ful play, as he had betrayed his strength twice already, first 
by raising before there was anything in the pot to speak 
of and next by standing pat, so that the others were already 
more or less afraid of him, and his refusal to raise was 
plainly a bid for a raise from some one else. It therefore 
failed to accomplish anything. 

E, knowing that A would almost certainly raise, also 
contented himself with coming in, and A raised it $5. He 
was also looking for D to raise, and the play had not been 
hard enough to provoke a raise of a greater amount. C 
had then to consider whether his three sevens were good 
against two pat hands, and very properly decided that they 
were not. He would have played them against two one- 
card draws and one pat hand, which he would have had to 
face if D had drawn one card, for he would have figured 
that the standing pat might be a bluff, and he would at 
least have stayed in on one bet, but his laying down was 
not only wise in view of the hands actually held, but it was 
good play, even according to what the game had developed. 

D had now only two to play against, and as E had not 
raised the first time, he hardly considered it likely that he 
would on the second round. Considering it, therefore, his 
last chance, he raised A $10. E, therefore, was in no posi- 
tion to raise, though he might possibly have done so if D 
had not, for while A might easily beat his ten high Flush, 
it might also be that the other two, A and D, both had 
Straights or smaller Flushes. As it was, however, both 
having raised, he considered that he was playing hard 
enough when he made good. He therefore trailed along. 

The struggle was now plainly enough between A and 
D. Had D drawn a single card, as most players do, holding 
Fours, A would have given him another raise unhesitat- 


I 3 2 


ingly, though he would not have pushed a deuce full too 
far, but as it was he hesitated for some time. Eventually 
he did raise $10, and so gave D his last chance, which he 
took advantage of by raising it $25. 

This put E in a hard position. He hardly considered his 
Flush good, but there was still a chance that it might be, 
and he had therefore to calculate the odds in the betting. 
There was $162.50 in the pot, and it cost him $35 to come 
in, with a possibility of a further raise. He would have 
been justified either in laying down or playing, but he de- 
cided to play. A also called and D of course took the pot. 
The difference between the character of his play and that 
of the holder of four tens in the other deal is shown con- 
clusively by a comparison of the results, for he took in only 
$222.50, of which he had himself contributed $66.50, leav- 
ing his winnings only $156. 

The holder of the four tens, however, had made a win- 
ning of $399. It is true that he was obliged to bet $236.50 
to do this, but the risk was too small to be seriously con- 
sidered in either case. It was actually greater in the smaller 
pot than it was in the larger, since there was a possibility 
of a Straight Flush being filled. This chance, even with 
a Four-Straight Flush out before the draw, is hardly 
enough, however, to deter any good poker player from back- 
ing Four of a Kind to the extent of his pile. 

The holder of the four Oueens made two distinct errors 
in his play, and it is worth while to consider how he came 
to make them, for they both came from his failure to 
grasp the opportunities or to understand the principles of 
play in the game of poker. In the first place, his raising 
when there was only $1.50 in the pot and four more players 
to hear from, including the age man, came from his sur- 
prise and premature exultation over a remarkably strong 
hand. Had he been a less emotional player he would have 


/ 


T 33 


seen the folly of what he did before doing it, but his im- 
pulse was too strong for him on the instant, and impulses 
are dangerous in poker. 

Again, in refusing to draw, as he might very properly 
have done if there had been only one player against him 
and that other player had already stood pat, he neglected 
to take into account the others who were playing, and the 
further fact that A had not yet been heard from and might 
not have a pat hand. In other words, he allowed his per- 
ception that A was his principal opponent to blind him to 
all the other chances he had. Even against a single player 
or a number of pat hands, the standing pat on Four of a 
Kind can hardly be considered good play, though it might 
be justified as tending to remove the chance of Four of a 
Kind being suspected. Even that would only be called 
good in case there was a moral certainty of a full hand at 
the very last being out, and it is seldom possible to judge 
whether a pat hand may not be a Flush or a Straight. 

One of the great beauties of Draw Poker is the faculty 
which it develops of rapid and accurate calculation of 
chances. Ordinarily the calculation has to be made on the 
basis of a hand that may not improbably be beaten, but 
when on occasions a hand is held which is almost certainly 
a winner, the good player will exert himself to the utmost 
to judge how to coax along not merely one antagonist, but 
as many as possible. The variations are infinite, but the 
principles are always the same. What is primarily required 
is the ability to judge whether it is better to force other 
players out or to retain as many of them as possible in the 
betting. 


134 


The Bluff. 

T HE underlying principle of the bluff in the game of 
poker is simple, but the practical execution of the 
successful bluff is something that calls for high skill. 
Like many other things simple in principle and theory, it 
involves details that are both intricate and difficult. All 
that is necessary to do is to convince your adversary that 
your hand is better than his, when you are yourself con- 
vinced that it is nothing of the kind. The proposition is as 
brief and sounds as easy as one could wish, but the one 
who undertakes a bluff without understanding is likely to 
grieve exceedingly thereafter. It is true that Draw Poker 
is full of surprises, and the most bare-faced bluff may some- 
times be successful, but this is by no means to be counted 
on, and when it occurs it is to be accepted as evidence of 
a lack of skill in the other players rather than as an achieve- 
ment of the bluffer. 

On the other hand, a bluff, provided it be done artist- 
ically, with due advantage taken of all favoring circum- 
stances and with just the right shade of insistency to secure 
the best results, is unquestionably the greatest achievement 
known in the game of poker. Since it is often essayed, 
even by good players, without due regard to the chances, 
it is worth while to analyze the various circumstances of 
the game that tend to defeat the bluffer, so that any player 
who desires to attempt the feat may know just what he has 
to contend against and what is most likely to bring him to 
confusion. 

Almost the first thing to be considered is the player’s 


i35 


position at the board with reference to the age. Unques- 
tionably the age man, or the player on his right, has the best 
opportunity for bluffing, and the man on his left has the 
poorest, so far as the position goes. Beginning before the 
draw the age man, if he be observant and if he have apt 
intuitions, can often form a judgment by the time he is 
called on to make his ante good as to whether there is a very 
good hand out against him. If there be, he will not, if 
ordinarily prudent, attempt a bluff before the draw. If, 
however, he shall decide that there is probably nothing par- 
ticularly strong in opposition to his own hand, he can often 
drive out two or three of his opponents by raising before 
calling for cards. Obviously, the fewer antagonists he has 
the fewer are the chances of his bluff being called. It is true 
that the pot will be the smaller for each player who fails to 
come up, but it must be remembered that the larger the pot 
is the smaller is the chance of its being won on a bluff. A 
small pot can frequently be won by bold betting without the 
cards to back it, whereas if there be a considerable amount 
at stake the chances are that some player with only a moder- 
ately strong hand will call, preferring to lose a little more 
money rather than see so much go without a struggle for it. 

If, therefore, the bluffer shall reduce the number of 

% 

players against him by having set up the presumption that 
his hand is really strong, his next step must be to strengthen 
that presumption as much as possible by the draw. It may 
be that some one of his antagonists has met his bluff with a 
counter-raise. In this case he has to consider whether this 
second raise is likely to be also of the nature of a bluff, or 
whether there is really a strong hand against him. If there 
be two raises after his own he will be wise to abandon his 
bluff as quickly as possible and either throw down his cards 
or draw to the strength of his hand, trusting to his chances 
in the draw. If, however, he shall have only a single raise 


to consider, it would be the part of wisdom in case he de- 
cides to go on with the bluff to raise again before the draw, 
since he will by doing this drive out all but the one player 
against him, and will deepen the impression as to his real 
strength in that one’s mind. 

If the second player again makes good, the presumption 
is that there is a good hand out against the bluffer, whom 
we may for convenience call A. A then has to decide as 
to his draw. If he be the age man, die is at a disadvantage 
in not being able to guide himself by B’s draw, but if he 
be the dealer himself, he can form some judgment by B’s 
draw of what there is against him. A has then to decide 
between standing pat or taking one or two cards. If he 
shall take three, B will know that he has nothing better 
than a pair of aces at the best, and he will weaken his bluff 
beyond remedy. Two cards give the impression of threes, 
which may be good play if B has drawn three, but stand- 
ing pat or drawing one is esteemed better poker, because 
standing pat leaves only one impression — that of a com- 
plete hand — and drawing* one leaves B a wide range for 
guessing. 

Hesitation, or any evidence of doubt or fear, is ex- 
tremely liable to ruin a bluff, and yet it may prove to be 
the most effective help to the bluffer if his antagonist have 
only a moderately strong hand. In that case, A, by pretend- 
ing to consider the chances doubtfully, may give B the 
impression that he really has a good hand, but fears that 
B has another, in which case B will not be likely to con- 
tinue betting unless he is also bluffing. If both bluff, of 
course the only question remaining is which has the more 
nerve. Neither one is likely to call, for the bluffer cannot 
call unless he is thoroughly satisfied that his antagonist 
is bluffing also. Even then, the show-down that follows is 
a betrayal of the original effort, and, therefore, extremely 


i37 




likely to impair the efficiency of any subsequent bluff by 
the same player. 

It may be said properly that any play in poker that goes 
beyond the mathematical chances of the cards actually in 
hand is of the nature of a bluff, and this is undoubtedly 
true. This is the reason why the best players usually con- 
fine their play to what they consider the legitimate demands 
of the cards they hold, bluffing only occasionally, and never 
unless the conditions are favorable. It may often happen, 
however, that a player will bet more on his hand than he is 
really justified in doing because of underestimating the 
hands against him. Probably this is the commonest fault 
in play generally. This, of course, is not bluffing, though 
it is practically equivalent to it. 

The reason why the best players rarely attempt to bluff 
unless the conditions are all favorable is to be understood 
by a brief consideration of the best results to be obtained by 
the bluff in ordinary play. In the first place, as has been 
noted, the bluff, pure and simple, is not likely to be success- 
ful when there is a large amount in the pot, especially if it 
be in a limit game. Almost of necessity, the amount put 
forth as a bluff must be disproportionate to that in the pot, 
for if it be not too large, some other player is likely to call, 
rather than see the money go without a struggle. The 
bluffer, therefore, excepting on rare occasions, must make 
up his mind to venture largely for comparatively small 
winnings. It is true that the winning of many small pots 
is likely to pay better in the long run than the winning of 
a few large ones, but the player who makes a habit of 
bluffing is sure to be detected and will be therefore at a 
disadvantage that will increase with every instance of his 
detection. 

But, if the carrying out of a successful bluff and the 
winning of a pot without the possession of the cards to 


138 


warrant the betting be the cleverest achievement of the game 
of poker, it must be said that the detection and defeat of 
a clever bluff is the next highest achievement. Not infre- 
quently it involves as much nerve, if not more, to call a big 
raise with only a single pair in the hand, as it does to make 
the raise with nothing better than ten high to go on. The 
truth is that every good player is constantly watching for 
symptoms of bluff in every other player's game, and the 
very fact that the bluff must always be made in the face 
of this suspicion increases the difficulty of the performance 
and enhances the credit of success. 

Stress has been laid on the importance of the player’s 
position relative to the age, and this may not be readily 
appreciated by those who are not thoroughly familiar with 
the game. For the sake of illustration, suppose six men 
to be playing, and the deal to be with A. The age, of 
course, is B's. If, then, C should think of bluffing, it would 
be manifestly absurd for him to begin before the other play- 
ers had come in. It is his first play, and if he makes a raise 
he has nothing to play for excepting B’s ante, which he must 
himself double before he can raise. Suppose the ante to be 
five cents, he must put up ten to play. If then he raises 
there is a chance that the others will all “ lay down,” and 
all he will win is five cents. But, if there happens to be a 
good hand out, as is likely, he will have a strong opponent 
and a poor hand to draw to. Evidently this game is not 
worth the candle. 

It must be remembered, however, that the advantage 
of position is always liable to change. Supposing D to 
have a good hand and to raise the limit. This may have the 
effect of driving out F, and A, E and B may come in, and 
C will then have the last say. lie has already come in on 
a small pair, and if he decides to bluff he has now an ex- 
cellent chance, even though there are presumably three fairly 


139 




good hands out against him. If he raises back the other 
three players are put on the defensive and must protect what 
they have put up before they can play. Their natural pre- 
sumption is that his hand is strong and that he did not raise 
at first for fear of driving them out. Against this there is, 
of course, the suspicion that always obtains against every 
play, that he is bluffing; but he has started his bluff favor- 
ably and has only to follow it up as well in order to win. 

His next step is not so easy. B draws first, so he knows 

0 

something about one hand. There are two others, how- 
ever, to hear from after he draws himself, and he must make 
all three think his hand is strong. Under the circumstances 
he will do well to draw two cards or stand pat. If he draws 
one he will be thought to be drawing for a Straight, a Flush 
or a Full, and will have to begin all over again the effort 
to make the others think he is really strong. In other words, 
he is relinquishing the advantage of the impression he has 
already produced, and this is an error. 

Having decided on his own draw he must watch that of 
D and E. Remembering that D raised first, he will be likely 
to credit him with a strong hand, since he was in a poor 
position to bluff. If D’s draw, therefore, be two cards 
he will feel sure that he had threes to begin. If D takes 
one card he will still credit him with threes or two good 
pairs at the least, though some players habitually raise on a 
Four Flush on a theory that is not entirely defensible. 

There is also a presumption that E is not bluffing, for 
if he had been, he would probably have raised D to keep 
the others out. And this reasoning applies equally to B. 
By watching their draw, C can form an approximate judg- 
ment of the hands he has to contest. 

C has now another disadvantage. It is his first bet, 
and if he decides to persist in his bluff, as he must do unless 
he is willing to stultify his previous play, he should bet the 


140 


limit, or if it be a table-stake game, make a large bet. If 
he put up a small amount he is likely to be called, but a 
large bet will drive out some of the three unless they are 
all strong. Should he be raised in turn he must either 
throw down or raise again, since he has no cards to call on. 

The essence of the bluff, therefore, is seen to be the 
accuracy with which a player can gauge the strength of his 
opponents and the quickness with which he can avail him- 
self of his opportunities. In this it differs no whit from the 
rest of the game of poker, but it is, as was said, the highest 
development of skill in the game. 


Punctilio of the Game. 


I MPATIENCE is often felt, and sometimes expressed, 
by poker players with others in the game who insist 
upon laughing, singing, telling stories or carrying on 
a running conversation while the game is in progress. The 
rules of the game, however, do not bar anything of this 
sort, and even the etiquette of the card table can hardly be 
said to forbid it. A player who chooses to do such things 
may say that he resorts to them as means of confusing or 
distracting his opponents' attention and so increasing the 
strength of his own hand, or rather diverting attention from 
it, and it is difficult to see what objection could be main- 
tained against the use of such means or of any other, short 
of physical interference with other players. 

Just where impropriety begins, when conversation of any 
sort is countenanced, is not easily determined, and as a 
matter of fact the law of etiquette is an elastic one. Poker, 
as was just explained, differs widely in this respect from 
whist, for example. In the latter game it is easy to interdict 
all irrelevant talk, but in poker a player may claim it as a 
part of his play. The only practical rule seems to be to 
withdraw from a game in which any of the players persist 
in talking or singing or the like to such an extent as to 
interfere with orderly play. 

One excellent plan has been devised for maintaining 
order among players who refuse to curb the exuberance of 
their spirits at the poker table or who believe that the kind 
of by-play indicated is a valuable addition to their game. 
Of course the only objection to such practices, as long as 


142 


they do not outrage propriety, is that they confuse other 
players and, by inducing small errors of play, make the 
game wearisome and uninteresting. The plan mentioned 
is, therefore, to impose a fine on each player who violates 
a rule of the game. This fine must be large enough to 
insure the attention of all the players and is usually fixed 
at a red chip, which is to be put into the next pot played for 
after the offence. 

It is indeed a question whether it would not be an ex- 
cellent expedient to agree upon some rule of this sort in 
every game in which there are careless or inattentive players, 
and even with inexperienced players the salutary effect of 
paying a small penalty for the infraction of a rule will be 
found to expedite the learning of those rules more than any- 
thing else. The fine should be small, of course. Probably 
a white chip for each offence would be ample, but once 
agreed upon it should be enforced mercilessly. As in the 
old-fashioned game of “ muggins/' no excuse should be 
allowed and no plea for mercy should be listened to. The 
player who has to pay for playing out of turn is sure to wait 
for his turn to come after he has paid the fine a few times. 

It should be clearly understood, however, that this levy- 
ing of a fine is no part of the game of poker. It can only 
be enforced by the common consent of the party playing, 
as there is no authority which can be invoked to compel 
the payment. 

While it is true, as explained, that the etiquette of the 
poker table is exceedingly elastic, and hardly anything short 
of rowdyism can be said to be actually barred from the 
game, so that common politeness may be said to be the only 
rule on the subject, it is also true that what may be called 
the minor rules of the game are to be enforced as strictly 
as any others, if the game is to be played properly. A cer- 
tain laxity in regard to some of these rules is often found 


M3 


even among* good players, blit the courtesy which allows 
the infraction of even the least important rule without pen- 
alty is a mistaken one, and any carelessness in this respect 
will certainly be followed by a deterioration in the quality 
of the play and a consequent loss of interest in the game. 
Even good players who seldom or never commit errors 
themselves are likely to overlook seemingly trivial errors 
in others, deeming it hardly worth while to insist upon an 
enforcement of the rules in small matters, but to do this 
is a mistake. It must be remembered as a fact of prime 
importance that it is just as easy to play poker correctly 
if one is paying attention to the game, as it is to play it in 
a slip-shod manner, and while it is just as easy for the 
individual in question, his attention to the rules makes the 
play much easier for others. 

For example, one error, perhaps the commonest of all 
that are made at the poker table, is playing out of turn. 
It is manifestly just as easy for one who intends throw- 
ing down his cards td wait until it comes his turn to play 
before doing so as it is for him to glance at his hand and 
finding it worthless to throw it on the discard pile with- 
out looking to see what the other players are going to do. 
The beginner always has difficulty in seeing the impor- 
tance of the rule which forbids him to do anything like 
this, yet if he throws down his hand before his turn comes, 
he is, very likely, doing a distinct injury to some other 
player who is still struggling for the pot, by giving his 
antagonist an advantage to which he is by no means en- 
titled. 

To illustrate this, suppose A, B and C draw cards, the 
others having dropped out, though there is a good jack-pot 
to play for. A has opened the pot on a pair of Jacks and 
fails to improve his hand in the draw. B, it may be, has 
come in, having also a pair of Jacks. He also fails to 


144 


improve, but gets an Ace ill the draw, A's highest card 
next to his pair being a King. C lias come in on a pair 
of nines and has also failed to better his hand. It will 
be seen that in case of a show-down B will win the pot 
away from the opener. 

A, desirous of giving the impression that he has a large 
pair, bets the limit before he looks at his draw. Possibly 
he has held up a kicker to give the impression of threes, 
and is really bluffing on his Jacks. C realizes that he has 
no possible chance to win except by bluffing on his nines, 
and feels that he has not the nerve to bluff against a pre- 
sumable Three of a Kind. Without regard to the rule, 
therefore, he throws down his cards before B has declared 
whether he will or will not play. Had C waited his turn, 
as he was obliged by the rules to do, B would undoubtedly 
have refused to bet, and the opener would have taken the 
pot. With C out of the game, however, B realizes that he 
has just one chance for the pot, and looking at it sees that 
there is considerable money in it. He therefore decides 
to take the risk, in view of the odds he gets in the betting, 
and calls A, winning the pot by virtue of his Ace. 

It is evident in such a case that B wins money that 
would otherwise have gone to A solely because of Cs mis- 
play. A has therefore a perfect right to complain. C, of 
course, has suffered no loss. He would not have won in 
any case, so he is personally unconcerned, though in equity 
he should be compelled to pay a heavy penalty. It is no 
defence for him to plead that as B’s hand was really the 
better one of the two, it is right enough for him to take 
the money, for this is not a correct proposition in poker. 
A pot does not always belong to the player who holds the 
best cards. If it did, all skill and the greatest part of 
the interest in the game would be eliminated, and poker 
would become as purely a game of chance as roulette. In 


r 


M5 

the case cited, although A showed no great skill, he cer- 
tainly displayed all the necessary nerve and really took 
longer chances than B did, since he bet against two oppo- 
nents, while B only called one. That, however, is not the 
real point of importance. What is important is that C by 
a violation of the rule gave B an opportunity to which he 
was not entitled. It was true that B showed courage in 
calling, but it was merely the courage of taking the small 
end of a bet because he thought the odds justified it. 

Another misplay which is often condoned and allowed 
as a matter of mistaken courtesy is the asking of one player 
by another how many cards he took in the draw and the 
answer which is given and allowed to- pass unchallenged. 
It is true that the rule on this subject goes no further than 
to prescribe that the dealer shall require each player to 
call audibly for the number of cards he desires and shall 
himself announce the number which he takes for himself, 
and that after the betting has begun he shall not answer 
any questions as to how many cards he has dealt to any 
player. As a matter of fact, however, the question is often 
asked and often answered, though never by good players, 
yet it cannot be answered truthfully without the possibility 
of giving some player an advantage to which he is not 
entitled over some other player. For no player is entitled 
to have his errors rectified or his memory refreshed when 
he is about to suffer loss by reason of his error or his lapse 
of memory. The moment he accepts a favor of this kind 
he becomes the recipient of charity and is put at an advan- 
tage over his opponents in the game who are playing on 
their own ability without asking favors. 

It would be easy to specify a number of other seem- 
ingly trivial matters in which even good players are likely 
to be good-naturedly indulgent of carelessness in others, 
but it is not necessary to do it. The truth of the matter 


146 


is that no detail of the game of poker, however trivial it 
may appear to be, can he neglected without deterioration. 
The most inexorable enforcement of all rules is the quick- 
est way to educate a new player and the only way to pre- 
serve the interest of the game among good players. 

But over and above this mere obedience to the rules 
stands the punctilio which dictates the observance of the 
spirit of those rules. It will be found by studying them 
that the one object of all of them is to guard the rights 
of each player jealously against any advantage to any other 
player beyond what he can get by superior skill or stronger 
cards. A punctilious observance of this spirit not only be- 
tokens true courtesy, but aids in maintaining Draw Poker 
as the best of all card games. 


147 


How to Play Jack-pots. 

T HE difference between Draw Poker as it is played 
straight, and Draw Poker as it is played for jack- 
pots, is more real than apparent. For, as the beginner 
views the latter variation — it is really a variation of the 
original game — he is likely to perceive no difference, ex- 
cepting that a pool is made up before the deal, to which 
all the players contribute equally, and it cannot be played 
for until some one in the game gets a hand of a certain 
value before the draw. These things, of themselves, he 
is likely to consider, make no essential change in the char- 
acter of the game, and to that extent he is undoubtedly 
right. It is not until he has studied the game carefully 
that he will see what radical differences in play are likely 
to be encountered in the struggle for a jack-pot, as com- 
pared with the ordinary game. 

Just how the jack-pot originated it is hard to say, but 
it is, legitimately enough, an outgrowth of the original 
game, and results from the spirit of fairness which rules 
Draw Poker. Formed in the regular way by default of 
play on any given deal it proved so attractive to most play- 
ers that it came to be called for arbitrarily, and in some 
circles it is played exclusively, while in others a “ buck ” 
is thrown into the pot, and being taken by the winner to- 
gether with the chips becomes the signal for the formation 
of the next jack-pot, which is made when the winner of 
the last one next deals. 

The first attraction is, naturally, that there is a larger 
stake to be played for. As this would be likely to inspire 


bolder play, and lead to unconscionable bluffing, the limit 
of a pair of Jacks, or something better, in the hand is fixed, 
below which the pot may not be played for. It was for- 
merly the rule that after the first deal, the pot having been 
sweetened, a pair of Queens was required to open ; after 
the second deal, a pair of Kings, and after the third a pair 
of Aces. The reason fo* this is apparent. The more money 
there is at stake, the greater the temptation to bluff. This 
rule, however, is now practically abandoned, and Jacks are 
held sufficient for openers at any time. Like all other 
changes in the game that have obtained permanent favor, 
this is a distinct improvement, for it does away with need- 
less confusion. 

The age is no less an advantage in the jack-pot game 
than in the regular, and as no player can be sure of having 
it until his left-hand neighbor has opened, some little ma- 
noeuvring is permissible and is held to be good play. For 
example, with seven in the game, and A dealing, B may 
have a good hand, say, two pairs, and may yet pass. His 
theory would be that in the six other hands yet to be heard 
from there will probably be openers, and he will have a 
chance not only to see how many competitors he has but 
also to raise the opener, thus declaring his own strength 
and swelling the pot. Supposing then that C opens, B’s 
finesse is well justified. Each of the other players must 
decide whether to play or not before he is called on to 
announce what he will do. Here is a manifest advantage. 

It is to be noted, however, that there is always a risk 
in passing with openers. It may very likely happen that 
no one else has openers, and B will therefore lose the op- 
portunity he had, in playing for an advantage which he 
may or may not get. Again, it may happen that A will 

r 

be the opener, in which case if B shall raise he will prob- 
ably keep the other five players out, whereas, having a 


149 


strong hand, he will desire a large pot. Moreover, his two 
pairs are likely to be beaten by any player who draws to 
a single pair. It is therefore counted risky play to pass 
with openers, and good players seldom do it unless there 
are at least four or five other hands to hear from. Even 
then, if the hand is exceptionally strong, it is accounted 
better play to open than to hold back for the possible chance 
of raising. To pass with Three of a Kind, for example, 
would be throwing away a substance in the hope of grasp- 
ing a shadow. 

* In opening, judgment should be shown in regard to the 
amount declared. To open for a small amount in compari- 
son to the amount already in the pot is an invitation to each 
other player to come in, regardless of what he has in his 
hand before the draw. To open for a large amount, on 
the other hand, will deter the others from coming in unless 
they have strong hands. It is therefore accounted wise to 
open for the limit, provided it be a limit game, unless the 
opener has so strong a hand that he does not fear competi- 
tion. If the game be unlimited or for table stakes the con- 
ditions are somewhat different, and more will be said of 
this presently. Of course the amount of competition to he 
desired depends on the hand held by the opener. If six 
out of seven players have passed and the seventh has Three 
of a Kind it would be good play for him to open for a 
small sum, provided his threes are Jacks or better. The 
chances are that no one has more than a pair of tens, and 
even if three tens should be obtained in the draw the opener 
will have no fear of them. It is therefore his policy to 
get as much in the pot as possible, even at the risk of being 
beaten by some exceptionally lucky draw. 

In opening a jack-pot, therefore, and in raising the 
opener as well, but especially in the latter case, the ques- 
tion of position must be carefully considered. It is true 




that position is an important element in all questions of 
poker play, but it is most especially to be remembered in 
jack-pots, seeing that the advantage of position is fixed, 
not by the deal, but by the opening, and seeing also that 
the fact of the opening amounts to a positive declaration 
that the opener has a hand of a certain minimum value. 

There are players who habitually raise on a Four Flush 
or a Four Straight, if it be a high one. The theory of the 
play is simple, but the play itself is too rash to commend it 
to most players, as it generally calls for a longer percent- 
age in the betting than there is in the draw. If the player, 
however, is careful to keep in mind the percentage of the 
bet he may easily determine at any time whether the ven- 
ture is justifiable. Supposing a Four Flush or a Four 
Straight to be in hand. The chance of filling is about the 
same in either case, being nine in forty-seven for the Flush 
and eight in forty-seven for the Straight, or between 5 to 
1 and 6 to 1 against. If, then, the hand when filled were 
a sure winner it would be good play to bet on the chances 
of filling it when better than 6 to 1 could be obtained in 
the betting. In other words, if there were $7, or even $6 
in the pot, it would be mathematical play to raise it a 
dollar. If no one sees the raise of course it wins. If other 
players come in, of course the odds become better. 

But it must be remembered that neither a Straight nor 
a Flush is a sure hand, though it is strong enough to justify 
betting, and there may be indications even before the draw 
that it is a doubtful hand to back. Unless the player, there- 
fore, can get odds of at least 10 to 1 in the betting, it 
is not advisable to bet on a Four Flush or a Four Straight. 
In the betting, however, it must always be remembered that 
what has already been put up is to be counted as odds 
against. Thus, if there be $10 in the pot, of which one 

player has contributed two, and he desires to put up an- 

• 


other dollar, he must not consider that he is getting 7 to 
3. The odds on the new bet are 10 to 1, for what he 
has put in is no longer his own. He has parted with it 
positively and irrevocably. It is no more his property than 
his next neighbor's chips are, excepting that he has a chance 
to win it. 

This method of calculation is never to be overlooked 
in poker, though inexperienced players are often confused 
in regard to it, and this confusion is likely to work in two 
directions. In one way it tempts a player to come in when 
his chances do not justify it, by leading him to think that 
his interest in the pot is proportioned to the amount he has 
contributed already, and in the other way it leads him to 
underestimate the odds he is getting in the new bet. The 
correct calculation is to consider each bet without refer- 
ence to what has been done before, and each chip that is 
put up is a bet, no matter whether it be an ante, a raise, 
or simply seeing another player's raise. Obviously, noth- 
ing but unusual luck can save a player who takes shorter 
odds in the betting than the odds against him in the draw. 

Reference has been made to the difference between a 
table-stakes game and one with a limit. This difference 
is greatly accentuated in playing for a jack-pot, when the 
temptation to bluff is the stronger by reason of the amount 
at stake. The comments that have been made already as 
to the advantages of position hold good, but the opportunity 
to bluff in a table-stakes game is of course much greater 
than with a limit, and this of itself changes the character 
of the necessary calculation. 

Supposing, as before, that there are seven in the game 
and A is dealing. B, having a pair of Jacks, may well hesi- 
tate about opening. Some players refuse to open on Jacks 
when sitting in this position, and some, indeed, will not 
open at all on Jacks. But if B decides to open, it would 


l S 2 


manifestly be poor play to put up a small amount. His 
hand is small and very likely to be outclassed even before 
the draw. His play then, supposing he decides to open, 
would be to put up such a sum as he thinks will be likely 
to keep the others out. Every player who is kept out means 
one chance less of beating his Jacks. It is well, then, to 
put up at least as much as is already in the pot, and more 
than that is better, though if he puts up too much he raises 
the suspicion that his hand is weak. There is a risk both 
ways and he must balance his chances. 

It may be said that putting up a larger stake than is 
already in the pot is risking too much to win too little, but 
it must always be remembered that many small winnings 
usually count for more in the long run than a few large 
ones. The player who takes too long chances because they 
are cheap, or who undervalues the winning of a pot be- 
cause there is little in it, will lose in the long run. 

In jack-pots, it will be seen, there are differences of 
play from that in the straight game, and these differences 
will be more and more appreciated the more the play is 
studied ; but it is also true that the rules governing the play 
and the principles of the game do not vary. The differ- 
ences come solely from the changed odds in the betting and 
the varying advantages of position. 

One question of importance should be considered before 
passing on from the consideration of the jack-pot. There 
is still in different clubs a decided difference in the rules 
regarding the splitting of openers in a jack-pot, or, in other 
words, the privilege demanded for the player who opens 
the pot, of discarding one of the pair on which he opened 
and taking his chances on filling another hand, as a Flush 
or a Straight, as, for example, when a player opens on a 
pair of Jacks, having the King, Queen, Jack and ten of 
one suit and the Jack of another. There is a distinct tempta- 


i53 


tion here to discard a Jack and draw one card, with the 
chance of making a Royal Flush, a King high Straight 
Flush, a King high Flush, or a King high, or Ace high 
Straight. 

In some clubs this is allowed and in some others it 
is not. In some clubs, when it is allowed, the discard pile 
is kept in proper order, and there can be no question after 
the pot has been won as to what the opener really discarded, 
each man being able to tell just how many cards he dis- 
carded, and the opener’s one card being, as it must be if 
the pile is kept in proper order, in its rightful place. This 
is actually the only way in which poker can be played so 
as to make the splitting of openers justifiable, if indeed 
it be justifiable at all. 

Unfortunately, the keeping of the discard pile in proper 
order is a detail of the game that is seldom insisted on, 
even by good players. Usually the cards thrown down are 
thrown at random, and are gathered up by some player 
who has passed out. Very commonly they are mixed up 
with the deck or that part of it which is not in the hands 
of those who are still betting, and the sequence of the dis- 
card is lost while the betting still goes on. 

This should not be done, strictly speaking; but as a 
matter of fact it is usually done, so that some other way 
lias to be found to enable the player who has split openers 
to show his original pair when he is called upon to justify 
his opening. Obviously there are only two ways of get- 
ting over the difficulty. One is to rely on his bare word, 
which poker players generally are reluctant to do, and the 
other is to require him to lay his discard on one side and 
guard it until after the pot has been won. In some clubs 
there is a rule that the opener may split the pair on which 
he has opened, but he must announce the fact that he has 
done so when he makes his draw. 


*54 


None of these regulations can be said to be entirely 
satisfactory, excepting that which calls for a carefully kept 
discard pile, and since players generally refuse to take the 
pains to keep the discard properly, it seems probable that 
the next important change that will be made in Draw Poker 
will be the prohibition of the privilege of splitting the open- 
ers. This is in the direct line of all the improvements that 
have been made in the game hitherto, and is therefore to 
be expected. As was said, the splitting is prohibited now 
in some clubs, and it is asserted that the number of players 
who object to it is increasing. 

One difficulty in the way of settling the question defi- 
nitely is that players by no means agree as to whether the 
opener of a pot ought, according to the spirit of the game, 
to be allowed to split the pair on which he opens. Those 
who maintain that he ought not to have that privilege say 
that the fundamental rule of the jack-pot is, that it cannot 
be played for unless a pair of Jacks or better is held by one 
or more players, and that if openers are split there is no 
guarantee of any hand at all being shown down on the 
call. 

On the other hand, those who uphold the practice say 
that the opener, having a pair of Jacks or better, is clearly 
entitled to open, and that if he chooses to relinquish the 
advantage of that pair and draw for a higher hand than 
he would be likely to get by taking three cards, he is doing 
it at his own risk and to his own disadvantage, and for 
that reason no other player has the right to object. 

There is good ground for argument on both sides of 
the question, and it may very possibly remain a moot point 
for a long time, though the privilege of splitting is likely 
eventually to be abolished. In the meantime, however, since 
it is very generally allowed, it is well to inquire under 
what circumstances it is good play to split openers. 


i55 


A pair of Jacks, while it is better than the average hand 
at poker, which is figured at eights or nines, is by no means 
a strong hand against more than one antagonist. It is 
therefore a common practice among good players to pass 
on Jacks when they have the first or second say in a party 
of five or more players. Some players indeed refuse to 
open on Jacks at all times, waiting for a better hand. 

It often happens that a player after opening on a single 
pair has reason to suppose that other players have him 
beaten before the draw. He may be raised and even raised 
more than once before cards are called for, and may have 
good grounds for the supposition that the raising is not 
a bluff. Or, if two or three other players draw before 
he does, he may see that he is likely to have a strong hand 
against him. 

To illustrate : A deals, B and C pass, D opens on Jacks, 
E stays, F raises, A raises again, and B and C both stay. 
In this case, F has probably aces at least, A has probably 
two pairs or better, while the chances are that B and C 
have each either a Four Straight or a Four Flush. In 
such a case D, if he has nothing but a pair of Jacks to draw 
to, will do well to lay down his cards. His chance of win- 
ning is too small to justify him in seeing the double raise. 
It may be, however, that one of his Jacks is a part of a 
Four Flush, even, as was supposed above, part of a Four 
Straight Flush. In such a case, while he is less likely to 
fill the Flush or the Straight Flush than he is to get a third 
Jack or a second pair, the hand he might fill by discarding 
a Jack and taking one card would be strong enough to jus- 
tify betting on it, and it might be good play to see both 
raises on the smaller chance. 

On the other hand, if B and C have both passed and 
D has opened on Jacks, and E and F have both laid down. 
A has come in and B and C have laid down, D would not 


be playing well to split his openers. He has only one antag- 
onist, and while A may have a better hand than he, the 
chances of bettering Jacks is greater than the chance of 
filling a Four Straight or a Four Flush. 

It may be said, therefore, as a general rule, that it is 
not good play for a player to split a pair of Jacks or better 
unless the play before his turn has come to draw has been 
such as to convince the holder of the pair that even a third 
to his pair would not be good for the pot. 


i57 


Caution and Courage. 

B EGINNERS in the game of Draw Poker who have the 
advantage of a tutor always receive the advice to 
play carefully. It is unquestionably sound counsel, 
for the game cannot be properly played without the exer- 
cise of great care. Caution, as well as courage, is a requi- 
site in the play, and a man who bets too boldly on a small 
Straight or Flush when circumstances indicate the presence 
of a stronger hand fails as completely in mastery of the 
principles of the game as he who lays down three Aces with- 
out an effort to win the pot. His failure, moreover, is 
likely to be more disastrous. Sound as the advice is, how- 
ever, it is productive of great bewilderment in the begin- 
ner’s mind, and not until he has learned to watch the indica- 
tions that are given by the play of his opponents can he 
easily distinguish between caution and rashness, because the 
same bet on the same hand will be conservative at one time 
and foolhardy at another. 

One or two fundamental rules should always be borne 
in mind, and the first of these is that there are only four 
really strong hands in the deck. They are the four Royal 
Flushes, which a player may possibly never see in actual 
play, though he be a lifelong devotee of the game. All 
other hands are only relatively strong, though a single pair 
is as potent, when nothing but a smaller pair is out against 
it, as the Royal Flush itself. This is, of course, an ele- 
mentary truth, but it is one that even experienced players 
are apt to forget when dazzled by the sight of unexpected 
fours, for example. 


* 5 8 


The second rule is also elementary, yet it is equally 
likely to be forgotten by the average player. It is that the 
player is never justified in making a bet on the strength of 
his own hand alone. He must always remember to take 
into consideration the chances of all the other hands. One 
who draws to Aces up and catches another Ace is natu- 
rally elated by the transformation of his hand from one of 
low grade to one at the top of the third grade, but he is 
not justified in betting on it without thought of the possi- 
bility of being beaten. It is true enough that an Ace Full 
is not frequently beaten, but on the other hand it is beaten 
often enough to mark the presence of actual danger, even 
though the danger be not serious. 

Possibly as good a study of caution and boldness as 
may be made is to be found in a certain play which some 
persons follow invariably under certain circumstances. It 
cannot be called cautious, but though bold enough it is 
certainly not rash. The circumstances are that the player 
in question either has the age or sits on the right of the age 
man, thus being, of course, the dealer. Some players, if 
they hold anything better than a pair of tens in either of 
these two seats, will raise when it comes their turn to come 
in, provided no one has raised before them. The theory, 
of course, is that a pair of court cards is better than the 
average hand, and consequently gives a favorable chance 
of winning, so that it is good play to swell the pot, that 
the winnings may be the greater. It might be said that 
this play stands on the dividing line between cautious and 
incautious play. It is sufficiently bold, since it shows that 
the player is willing to back his chances when he has them, 
even though there are strong chances against him as well 
as in his favor in the draw, but it is not too bold, since 
his own chances are as good, presumably, as any one’s else. 
The really cautious player, however, would scarcely raise 


i59 


before the draw, even though he had last say or next 
to the last, on anything less than two good pairs. If, how- 
ever, he should refrain from raising on Aces up when he 
had the advantage of position, his play would be called 
timid unless he preferred to conceal his strength, as some 
players do, until the betting after the draw. 

It is to be noted, however, that although a definite 
statement can be made concerning this or that play before 
the draw, as to whether it is bold or cautious, no such 
statement can be made of any given play after the draw, 
without taking all the circumstances into consideration. An 
example of this may be cited in a play that would be con- 
demned off-hand by nine players out of ten as extremely 
timid, but which is to be supported with no weak argument. 

There were six in the game. A drew three cards and 
caught a third fourspot to his pair. B and E each drew one 
card, C and D each drew three, and F drew two. F had 
the age. After the draw A bet a white chip. B threw down 
his cards. C raised it the limit. D, E and F saw the raise 
without raising again, and A had the last say. Instead 
of seeing the bet as he might have been expected to do, 
having Three of a Kind, he threw down his cards. “ Ordi- 
narily,” he said, “ I would have called as a matter of course, 
even if I had not raised; but the cards had been running 
extremely high for half an hour, and I figured the prob- 
ability to be that there were threes out against me, in which 
case there were ten chances of being beaten to two of my 
winning. My three fourspots were too small.” 

The show-down proved that he was right. C had three 
Jacks, while D, E and F each had two pairs. This, of 
course, did not of itself prove the soundness of his play, 
for perfectly sound play is often unsuccessful in poker, 
while ill-judged ventures are often successful, so that no 
play can be called good because it captures a pot, neither 


i6o 


can any play be called bad because it has failed to win. 
It did show, however, that C had been correct in his judg- 
ment, even though he had founded it on so delusive a thing 
as a run of the cards. 

This matter of a run of the cards, it must be clearly un- 
derstood, is probably the most puzzling thing connected 
with the game of Draw Poker. As a matter of theory, of 
course, the chances in any one deal, the same number of 
hands being dealt, are exactly the same as they are in any 
other one deal. Practically, nothing is more certain than 
that the cards often run in series of hands, either good or 
bad, and that these series frequently last for a dozen deals 
or even a hundred or more. While one of these runs, so- 
called, is in progress, any calculation on the averages that 
are made from thousands and tens of thousands of hands 
would be wholly at variance with the probabilities. It is 
nothing uncommon for the same party to play for half 
an hour, for example, without seeing a hand larger than 
a Straight, and in the next half hour to see a dozen or 
more Fulls and Flushes beaten. Such unevenness does not 
in the least affect the average which must serve as a basis 
for any comprehensive understanding of the game; but it 
does, on the other hand, materially affect the play of any 
man who has a practical knowledge of it. 

To judge therefore of the degree of caution to be exer- 
cised in order to escape the charge of rashness it is neces- 
sary not only to estimate the relative excellence of one’s 
own hand, as considered according to the law of averages, 
but also to consider the chances of each opposing player, 
as indicated first by the law of averages and then according 
to the indications he may have given by the number of cards 
he has called for in the draw, and by the amount he has 
bet and the manner in which he has made his bets. More- 
over, there is a judgment to be formed according to one’s 








i6i 

knowledge of each player’s personal characteristics, so that 
a two-card draw by one player may be a tolerably sure in- 
dication of Three of a Kind in his hand already, or it may 
mean that he is drawing to a Bobtail Flush or a single pair 
with a kicker. His raise to the extent of the limit may mean 
a bluff or it may be a dangerous sign. 

And more than all these things, the experienced player 
learns to judge of the value of his hand by the way the cards 
are running. This comes to be almost intuition, so that 
Three of a Kind, as in the example cited, will seem a small 
hand at one time, whereas at another time they would call 
for a substantial raise, and this entirely aside from the 
indications given by the other players. 

Timidity, therefore, is not necessarily shown by the 
laying down of a comparatively strong hand, especially if 
many strong hands have been shown in the deals imme- 
diately preceding. On the contrary, as has been said often, 
it is one sure sign of good play when a man lays down a 
strong hand because of his belief that there is a stronger 
one against him. His judgment may not be correct, and 
in that case he will be, of course, a loser, but the fact that 
he relies on his judgment sufficiently to face the loss of 
what he has already put into the pot rather than to risk 
additional money against his judgment is a clear indica- 
tion that he possesses at least one qualification of a good 
player. 

The average player is perhaps more likely to display 
caution in calling a bet when he feels that he has a fair 
chance, than he is by laying down his cards. The question 
of when to call is no less important than that of when to 
raise and when to lay down. As a matter of fact it is prob- 
able that more mistakes are made in calling than in any 
other way. The player must never forget that he is playing 
solely on his judgment of the relative strength of two or 


f 


more hands, including his own. If he bets against his judg- 
ment he is abandoning the only guide he has in the game, 
and if he fails to back that judgment he is lacking in cour- 
age. The mistake is often made of calling after one has 
fully decided that his own hand is the weaker of two, and 
the impelling motive is a reluctance to see another win the 
money he has himself put in the pot. This is poor play 
because, as has been explained before, the money in the pot 
has gone out of the player’s possession already. He has 
no ownership so far as his own contribution goes, any more 
than he has in the contributions of his antagonists. If, 
then, he shall call because he has already bet more than 
his present judgment approves, he is accentuating his 
former error by committing another. And if he shall call 
when his judgment is positive that his own hand is the best, 
he is erring on the side of undue caution, which is well- 
nigh as serious a fault in poker as recklessness. 


f 


\ 



The Covinter-Blviff. 

I T is a comparatively simple thing* to learn the game of 
poker well enough to play it, if such a thing were 
possible, in the absence of opponents. That is, the 
theoretical play, based upon the rules of the game, the 
doctrine of chances and the cards in one's own hand, is 
easily enough mastered, so that the player will have no dif- 
ficulty in formulating his own course of action at any time 
when he happens to have the first say after the draw. But, 
although this knowledge is essential to an understanding 
of the game, it is of little practical value unless it is sup- 
plemented with an understanding of the play of others. 
At the very outset of the play there begins a struggle be- 
tween opposing wits, in which each player is compelled to 
watch the tactics of his opponents with as close attention 
as a swordsman has to pay to the motions of his antagonist 
in a duel. 

Because of this antagonism, in which the sole end to 
be attained is an opinion as to the probable strength of the 
other man’s cards, it is of prime importance to observe as 
closely as possible the habit of every man’s play, and it is 
also important, perhaps equally so, to conceal one's own 
habit. Because of this it should be remembered that it is 
bad play to show any hand unless the rules of the game 
require it to be shown, and it is also bad play not to insist 
on seeing each hand which the rules require to be displayed. 

This is a point on which even experienced players are 
apt to be lax. Nothing is more common than to see hands 
shown down which have not been called, and to hear this 


164 


play and that criticised and discussed when the player was 
not obliged to reveal the line of reasoning which he adopted. 
Whenever that is done the player who has shown his cards 
contributes to the benefit of his opponents by telling them 
in effect just what his line of play has been on one occasion, 
and so enabling them to judge of what it is likely to be at 
some other time. The rule is simple and explicit. The 
hand of each man who is in at the time of the call must be 
laid on the table face up, so that each person in the game 
may see what each man has seen fit to play on. But no 
hand which a player refuses to back to the extent of a call 
need be shown, nor is it required to show the winner’s hand 
unless he be called. This, of course, does not apply to the 
rule compelling the opener of a jack-pot to show openers. 

It is therefore loose play to show even a phenomenally 
good hand, such as might surprise the party, when it has 
won a pot without .a call. Still worse is it to show a 
worthless hand after the player has successfully bluffed 
on it. It only serves as a guide to one’s opponents. On 
the other hand, it is very common to hear a player, after the 
call, when his opponent has declared his hand, say, “ That’s 
good,” and throw his hand, face down, in the discard pile. 
This will never be allowed by good players, who have a 
right under the rules to know whether he has been bluffing 
or has been guilty of bad judgment in backing a hand too 
heavily for its actual strength. The man who does not 
insist on all his rights at the poker table is extremely likely 
to have them ignored. 

The importance of seeing all called hands lies in the 
opportunity, given by the display, of judging of the habits 
of other men’s play. When you know that a player is in 
the habit, for example, of holding an extra card when draw- 
ing, you may often judge of your chances in drawing 
against him better than you could otherwise. One trick of 


play is common with many players, of standing pat on an 
incomplete hand, such as two pairs, or a very weak hand, 
such as a pair of Jacks after opening a jack-pot. The object, 
of course, is to give one’s opponents the notion that the 
player has at least a Straight, and an opponent who believed 
that would, of course, throw down three Aces or anything 
less, without even a call. If he knew that the opener was 
a habitual bluffer he would call on a comparatively small 
hand. 

An example of how this knowledge of a man’s game 
helps his opponents is given in a certain play which has 
been described elsewhere. The gamesters who believe in 
it will invariably raise before the draw if they chance to 
have a pair of Jacks or better, and to sit in the age seat, or 
next to it on the right. This is a rule of play that has de- 
cided merit and will win many pots if properly backed by 
subsequent play, but there is a counter to it equally strong 
which will also win money in many cases for him who 
plays it. 

Let it be supposed that there are six playing and that 
A has the deal. B has anted and C, D, E and F have come 
in. A, having two Jacks, raises the limit. If the others 
do not know his play, they may not improbably all drop 
out, thus giving him a small winning, it is true, but an 
easy one on a small hand. But if it be known that A is 
in the habit of raising thus on a comparatively small hand, 
the others will be likely to come in if they have any reason- 
able prospects in the draw. Suppose that each draws three 
cards except A, who, having the last draw, still looks on his 
Jacks as reasonably good, and draws two, seeking to give 
the impression that he has Three of a Kind. C may bet 
a single chip and D and E drop out. This gives F, if he 
shall have caught a third to his pair, an opportunity for 
some good play. If he be wise he will simply see the one 


i66 


chip that C has put up and wait for A to raise, as he prob- 
ably will do, to carry out his play logically. If B and C 
see the raise, F will then be justified in raising again, with 
the expectation of making more than he would have made 
by raising the first time he had the chance. 

This really amounts to the use by F of his knowledge 
of A’s habit of play as a means to win A’s money. The 
example is a simple one, but it illustrates one way in which 
this knowledge is useful, and there are hundreds of such 
ways, for the game is one of unlimited variety. 

The habit of bluffing is one that many otherwise good 
players form, and it is of all habits the hardest to conceal, 
since the habitual bluffer is almost certain to be caught 
often enough to raise a suspicion of any play he may make, 
even on a good hand. Obviously if a man could always 
remain undetected, the bluff would be the simplest and 
easiest way to win at poker, but since it is almost impossible 
to bluff frequently without being called, and thus exposed, 
the good player will attempt the feat seldom. Each suc- 
cessful bluff, however, constitutes a temptation to repeat 
the effort, and the player who succumbs to the temptation 
too frequently is almost certain to come out of the game a 
loser. 

There are two ways of countering the bluff, and the 
choice between them is a matter calling for first-class judg- 
ment. This judgment, moreover, must be not only in re- 
gard to the probable strength of the cards in hand, but also 
in regard to the habit of the bluffer’s play. The simple 
call is, of course, immediately effective and is usually em- 
ployed as the counter when the player believes that another 
man is bluffing, but at the same time has no great confidence 
in his own hand. It requires courage to call, of course, 
when one has a small hand, but it is often good play when 
a bluff is suspected, unless the amount to be put up for 


a call bears too large a proportion to the amount in the pot. 
When the limit is small, this is seldom the case, so that a 
call is tolerably sure to come, and the bluff is seldom suc- 
cessful. It is of little use to bluff in a small-limit game. 
Th 1 ; reason is that the man who wishes to call can usually 
get a good percentage on the necessary bet. 

In using this first-mentioned counter to the bluff, there- 
fore, only a simple calculation is necessary. The amount 
in the pot can be seen at a glance, so that the odds of the bet 
are apparent. If they are sufficiently large to balance the 
probabilities of the suspected bluffer's really having the 
winning hand, there is, of course, only one thing to do, 
and that is to call. It is therefore self-evident that any 
knowledge you may have of the bluffer’s habit of play will 
be of advantage to you in deciding whether to play. 

It will be seen that a bluff to be effectual should be 
made for a large sum, in comparison to what is already in 
the pot, and the bluffer will bet in conformity with this 
idea, generally speaking. The natural result is that if he 
bets too heavily it becomes at once apparent that he is prob- 
ably bluffing, and he is tolerably certain to be called. The 
question of how much to put up to make the bluff effect- 
ive without overdoing it calls for nice judgment. 

The second counter of the two mentioned is to bluff 
the bluffer. This is one of the boldest things to be done 
in poker and is not to be attempted by any player who is 
not fully confident of his own nerve and at the same time 
confident that the other's nerve will fail. Take a deal in 
which all have passed out but A and B. There is $i in the 
pot, and A, having only a small pair in his hand, decides 
to bluff. If he raises 50 cents he will expect B to call if 
he has, say, tens or better, which he is very likely to have. 
If A should raise it $2, on the other hand, B would imme- 
diately suspect a bluff and would be all the more likely to 


i68 


call. A raise of $i would be, however, large enough to 
deter B from calling unless he had a strong hand, because 
the $2 in the pot would only give him 2 to i against the $1 
required for a call. And at the same time it would not be 
a larger bet than A would naturally make if he had a strong 
hand and wanted to get as much as possible on it. 

The bet of $1, therefore, is probably what A would 
make, desiring to bluff on his small pair. B will suspect a 
bluff, since the good poker player always suspects his op- 
ponent of bluffing and allows the suspicion as much weight 
as the circumstances indicate. With his own hand of a 
pair of tens he does not feel himself justified in calling, 
and at the same time he has a feeling that he would prob- 
ably win if he should call. This is a good place for the 
counter-bluff, and he raises A $2, hoping to frighten him 
out if he really was bluffing, and to intimidate him in any 
case. 

This, as was said, is bold play, and brings out one of 
the most interesting situations of the game, in which 
neither player is betting on the actual strength of his own 
hand, but on his distrust of his antagonist, and on his con- 
fidence in his own superior nerve. The issue will depend 
entirely on the manner of the two men's play, and their 
confidence each in his own judgment. It is entirely dif- 
ferent in character from the contest which is seen when 
each man has a strong hand and honestly believes it to 
be stronger than the other. 

Play is always met with counter-play, as was explained, 
and the careful poker player will lose no opportunity of 
studying the ideas, habits, and even the superstitions of 
his antagonists. It is only thus that he can devise his own 
counter-play effectively or understand the nature of the 
other man’s. 


169 


Playing AgaJnst Odds. 

T HERE is one phase of the game of poker which pre- 
sents a temptation to the beginner, and against 
which, in all fairness, he ought to be warned, lest 
unthinkingly he be subjected to serious loss and inconven- 
ience at a single sitting. If he play oftener, or for heavier 
stakes than he ought, the game is not to be blamed; but 
it does not seem altogether unfair to blame the game if 
the fascination of the moment carries him unthinkingly 
off his feet, so that he loses his mental and moral equilib- 
rium for the time being. 

It is to be noted, however, that the player must be- 
ware especially of the temptation to continue his play in 
the hope of recouping his losses, when the odds are in 
reality against him and he has already lost more than he 
is willing to do. It may be said that no man is willing 
to lose at poker, but certainly no man can expect always 
to win, and he who is not willing to lose sometimes does 
not play poker for the game, but for the stakes, and is 
a gambler rather than a gamester. 

This temptation is a strong one, and often proves too 
strong even for good players. The possibility of winning 
is especially alluring when the winning seems an actual 
necessity, and even level-headed players are often found 
revising the principles of good play and taking longer 
chances, for the simple reason that the chances are running 
against them, instead of waiting for strong hands and good 
opportunities as they should do. 

The poker player who watches the game as it should 


be watched will not be long in doubt of the fact if the 
chances are really against him, instead of being equal with 
those of the other players, as they should be in theory. 
If he lose money steadily for a while he will be almost 
certain to declare that the cards are running against him 
and this may indeed be true. The one phenomenon of the 
game which can never be explained is the fact that any 
player in any game is liable to get a long series of remark- 
ably good or remarkably poor hands. It may happen, of 
course, that good hands may run to all the party, or that 
there will be few good hands held by any one during a 
considerable time, but the unexplainable thing is the con- 
tinued bad luck or good luck of some one player. This 
will often continue through an entire sitting or a series of 
sittings and it is even true that some players seem never 
to get cards equal to the average, while others will aver- 
age, year in and year out, much better cards than their 
opponents. Why this should be true, as was said, cannot 
be explained on any theory, but no experienced player is 
likely to deny that it is. 

There are two courses for the player when it has be- 
come apparent that the cards are actually running against 
him. He can quit the game, which is really the prudent 
thing to do, since no skill is likely to avail him much 
without at least a fair show of cards. Or, if desirous of 
playing, and willing to wait for a turn of luck, which will 
probably come sooner or later, he may continue in the game 
without serious loss if he will control his play firmly and 
not undertake to force the luck. 

In doing this he should, whenever it is his turn to make 
the ante, put up the smallest amount allowed. A single 
white chip is sufficient, and will really answer his purpose 
as well as a large sum. It is true that any other player, 
when it comes his turn, may raise, but the ante man is not 


obliged to make good, and if he has no encouragement in 
his hand to draw he will escape with the minimum of loss. 
On the other hand, if he has good cards, he can raise at 
the time of making good, and so test the hands opposed 
to him. Obviously this advantage is not open to him when 
a jack-pot is to be played, since he must put up his quota 
to get cards, but he can then apply the second rule of 
safety. He cannot play without some loss till his luck 
shall turn, and he is only concerned in making that loss as 
small as possible. 

He should then refuse to draw cards on anything less 
than a pair of tens at the very least, and in jack-pots on less 
than openers. And, having drawn, he should refuse to see 
any bet whatever unless he shall have bettered his hand. If 
it be his first say it may be well to venture a chip on the 
chance that no one else has a hand worth playing, but if 
any one else shall raise he will be foolish to call unless he 
strongly suspects a bluff. 

If it be objected that this is not playing poker, the re- 
ply is that a man should not play poker while the luck is 
positively against him. The only thing open to him if he 
does not withdraw is to stay in the game at as little expense 
as possible and this he can only do by refusing to bet until 
he gets cards to bet on. An impetuous man will find this 
difficult to do, and will be constantly tempted to take long 
chances in the betting with the hope of some sudden luck 
in the draw. If he be one whose temper is likely to get 
the better of him he will become exasperated by his ill 
fortune and will continue to chip in thus until his losses 
have been serious. 

The game is played very differently by different peo- 
ple and if the play be what is called open — that is, if all 
in the party are betting freely in excess of the legitimate 
value of their cards — the danger to the man in bad luck 


IJ2 


is even greater than it is in a less liberal game, since he will 
be almost sure to be influenced by the play of the others. 

But although the player is likely to declare that it is 
the fault of his luck when he is beaten, and, although this 
may often be true, it is still more likely that his losses are 
attributable to his system of play or to the fact, which no 
player likes to acknowledge, that he is outclassed in skill. 
It may easily be that more experienced players than he 
can read his play well enough to tell with almost unfailing 
certainty when it is safe to bet against him and when he 
has really a strong hand. It is a test of a man's character 
to place him in a position of this kind, since he will be 
unwilling to admit the truth of it if he be vain, and un- 
willing to act upon his knowledge if he be obstinate. If, 
however, he be clearsighted and understand the game well 
enough to analyze the play from hand to hand, he will usu- 
ally perceive the fact when he is fairly outplayed, and then 
if he is wise he will either retire from the game or continue 
in it for the sake of improving his play, exercising at the 
same time all the caution he can command. 

Most likely of all the unsuccessful player has his own 
system to blame for his losses. While it is true that few 
players follow any general rule of play inflexibly but vary 
their drawing and betting according to circumstances, it 
is also true that every man who plays frequently has a sys- 
tem of his own, whether he is conscious of the fact or not. 
And it is by the small errors of these systems as they are 
commonly pursued that the weakness of the average man's 
play is manifested. Let a player keep account of his play 
for a single sitting of three or four hours and he will al- 
most certainly find that he has lost more money by play 
which his judgment does not approve than he has by bet- 
ting on hands which he had reason to believe good enough 
to bet on. 


i73 


The first and commonest error is in paying to draw 
cards when the player has not as good a hand as one or 
more others probably have. In a game of seven players, 
for example, the chances are that one or more players will 
have at least as good a hand as a pair of Jacks. This is 
shown by the fact that with seven playing in a jack-pot 
it is usually opened on the first deal. Occasionally it will 
not be, but as a rule it will. Manifestly the jack-pot has 
nothing to do with the falling of the cards, therefore a 
player who pays to draw cards to less than a pair of Jacks 
is putting himself at a disadvantage before the draw. He 
will probably be beaten. It is true that he may improve 
his hand, but his chance of doing so is no better than that 
of the man who starts with a better hand than he has. 
Then if both improve in the draw he is still at a disadvan- 
tage. To continue, therefore, to draw cards to a hand that 
is probably outclassed is to invest money without an equal 
chance of getting it back. 

Next to this error comes the habit of betting on cards 
that are probably inferior. If a man sits next to the age, 
and has therefore the first say, he will commonly put up 
a bet of some sort, large or small, whether or not he has 
improved in the draw. Sometimes, of course, he will win 
by it, since there will be times when no one else has bet- 
tered, but if he bets thus on a small hand he will usually 
lose, and the repeated loss of small sums will soon over- 
balance the occasional winning that he may make. It is 
more profitable in the long run to throw down poor cards 
without betting than it is to venture even a small bet on 
them in the hope, which may occasionally be realized, that 
all the hands out against them may be even of less value. 

The third, and perhaps the worst error of the three, is 
the habit many players have of calling an opponent's hand 
without a justifiable belief in the strength of their own 


174 


cards. A bet may have been made in the first place with 
good judgment, based on reasonable grounds, but subse- 
quent play may indicate clearly that the opponent is either 
bluffing or has the superior hand. In this case it some- 
times calls for critical judgment to decide whether there is 
actually a bluff, in which case the first player would of 
course call, or whether it be a genuine case of strong cards. 
Here is a temptation, and a strong one, to call anyhow, 
lest the other man steal the pot. But the moment a player 
formulates a rule of play according to which he shall always 
call in such a case, that moment he commits himself to a 
hopelessly bad course of play. He must remember that his 
judgment is all he has to rely on, and when he bets against 
his judgment, even if it is only by calling to determine 
whether or not the other man is bluffing, he is playing 
against himself and against his only chance of winning. 




175 


Calling 0Li\d Raising. 

I T is accepted as an axiom by many poker players that 
“ a hand that is strong enough to call with is strong 
enough to raise on.” Whether the saying has or has 
not all the truth which would entitle it to be classed as axio- 
matic, it cannot be denied that there is some truth in it, 
for without some reason for supposing that his own hand 
is better than that of his antagonist no good poker player 
would think of calling. And if he has reason to think that 
he holds the stronger hand he is justified in raising. The- 
oretically, therefore, it would almost seem as if there ought 
to be no such thing as a call in a well-played game of poker, 
but that each and every pot should be relinquished by the 
last player, who finally concludes that his own hand is the 
weakef of the two. And in case each of two or more play- 
ers should think with good reason that he held the best 
cards out, good play would require that the betting should 
continue indefinitely. 

Practically, this is absurd. There are different reasons, 
each of which may justify a call, though it is undoubt- 
edly true that the poor player is likely to lose more money 
by calling without good grounds for doing it than he is in 
almost any other way. It must be remembered in the first 
place that even if a player believes he has the best hand, 
it does not necessarily follow that it is good play for him 
to bet indefinitely on the strength of it. There is a point 
beyond which ordinary prudence will prevent a player from 
betting on any hand short of a Straight Flush, to say noth- 
ing of the ordinary common sense that ought to prevent any 
man from playing beyond his means. 


176 


In the second place, it must be remembered in backing 
any hand that the player has to take into consideration not 
only the hands which he thinks are opposed to his own, but 
also the possible chance of an error in his judgment and the 
still greater chance that one of the accidents of poker has 
happened, and that his opponent has filled a wholly unex- 
pected hand. These possibilities are never to be left out 
of account, so that it becomes a habit with most players 
not to bet on any hand further than the amount, roughly 
speaking, which they consider such a hand worth. When 
once they reach that limit, it is common to find them call- 
ing, not because their judgment has been shaken as to the 
probability of their own cards being the best, but because 
on general principles it is not good play to invest too much 
money on any single chance. 

Expressing this in other words, it may be said that a 
player must always calculate on having against him not 
merely the hand which his opponent may reasonably expect 
to make in the draw, electing to take one, two, or three 
cards, but the hand which he may possibly have made by 
one of the lucky accidents which are always liable to hap- 
pen in the game. 

An extreme illustration of this would be in the follow- 
ing example of actual play. The hands held, considering 
the draw, were certainly unusual, but not sufficiently so to 
be called remarkable. Six were playing, but when A 
opened a jack-pot all passed out excepting F, who raised 
it, he being the dealer. A saw the raise, having Kings 
and eights, but decided not to raise back, preferring to 
wait till after the draw, that he might judge as to what F 
had raised on. 

In the draw A caught a third King, making a Full 
Hand. F, who had raised before the draw, took three 
cards, making it almost a moral certainty that he had raised 


177 


on a pair of Aces. The game was table stakes, and each 
man had about $100 in front of him. A, having full con- 
fidence in his hand, but not desiring to frighten F out of 
the betting, put up v$io. He argued that if F had not bet- 
tered his hand he would lay it down against a one-card 
draw, but if he had bettered it he would probably raise, in 
which case he would probably have Aces up or three Aces. 

A was delighted to see F put up $20, being a ten-dollar 
raise, and giving him credit for three Aces, promptly saw 
the raise and pushed forward $25 more. F then saw this 
raise and raised again, $25. 

This made a case in which A had to consider the 
strength of the saying that a hand good enough to call on 
is good enough to raise on. He had a King Full, which 
would certainly be strong enough to call on, even against 
the improbable chance that F might have an Ace Full, 
the odds being decidedly against any such contingency, and 
the odds in the betting being the other way. This last was 
certainly the case, for there was $15 in the pot before it 
was opened and $65 before the draw. With the betting 
up to this point, there was $130, against which he had only 
to put up $25 if he should decide to call. No poker player 
would lay down in preference to this bet, under the cir- 
cumstances, and all he had to study was the advisability 
of raising again. 

The average player would probably have raised, but A 
hesitated. He knew his own hand was strong, and he felt 
certain that F had drawn to a pair of Aces, in which case 
he was either bluffing or had bettered his hand materially. 
His confident play made it probable that he had better than 
three Aces, for even with them he would hardly have 
pushed the betting as far as he had against a one-card draw. 
A knew him for a cautious player, and felt sure from his 
betting that he had better than threes, which would be, con- 


178 


sidering his draw, either a Full House or Four of a Kind. 
If it should be a Full, it would either be an Ace Full or 
one that A’s hand would beat, but if it were one or the 
other, the chances were equal of its being an Ace Full, since 
he was just as likely to have drawn an Ace and a pair as 
three of one denomination. If it should be fours he had 
caught, of course A’s hand was worthless. 

This brought the personal equation into the problem, 
for A had necessarily to consider the play that F had al- 
ready made, and taking that into consideration, he figured 
that there was a strong chance of his King Full being 
beaten. Under the circumstances, he felt that the rule did 
not hold good. He was not strong enough to raise, or he 
felt that he was not, but with the odds of $130 to $25 in 
his favor, he felt that he was strong enough to call. 

Accordingly he called, and F showed down four Aces, 
of course taking the pot. In this case it certainly appeared 
to be demonstrated that A’s reasoning had been correct, 
and that he was up against better than three Aces. Since 
he had no means of knowing whether it was fours, an Ace 
Full, or a smaller Full than his own, he was certainly justi- 
fied in calling, while it was, to say the least, very question- 
able whether he would have been justified in raising. The 
result, while it indicated that he had been wrong in calling, 
was no proof of that proposition. On the contrary, al- 
though he was really up against four Aces, he had no good 
reason to suspect it, and his calling with a King Full was 
evidence of cautious instead of reckless play. It must be 
remembered always that it is no proof of bad play to lose 
a bet in poker. If the bet is made after the exercise of 
good judgment, and the recognition of all the chances for 
and against success, it is merely an action taken in view 
of the odds in the betting. In this case, although A lost, 
he was really making a bet in which the odds in his favor 


179 


were greater than the chances against him, although, as 
already shown, he did not feel that they were sufficiently 
greater to justify a raise. 

Without going over the same ground too often it should 
be said that the beginner in poker has to learn to resist the 
temptation to call. This temptation comes in two forms, 
one entirely foreign to the game as it should be played, and 
the other based on a plain misunderstanding of the truth. 
The first is simple curiosity. A player has a hand which 
he has considered strong enough to bet on, and has accord- 
ingly put up his money. Some other player has raised him, 
and he feels that it is an open question whether the other 
player is bluffing or whether he has really the stronger 
hand. The first player does not feel strong enough to 
contest the matter further, but he has a curiosity to know 
what the other man is betting on. He may try to justify 
himself by saying that he is studying the other man's play 
when he calls, but such an occasion makes the study too 
expensive to be profitable. He must remember that curi- 
osity has no place in poker, and will ruin any player who 
allows it to get the better of him to such an extent that he 
will spend his chips to gratify it. 

The other inducement which will often make a be- 
ginner call when he ought not to, is the calculation of 
what he has already staked in the pot. It may be that 
he has already bet, say $2, and it costs him only $1 more 
to call. The natural thought is that the fact of having 
$2 already at stake justifies putting up another dollar 
to protect the two, but this is entirely erroneous. What 
has already been bet by the player himself has nothing what- 
ever to do with the question whether he shall bet again. 
What is in the pot belongs in no sense to the man who 
put it in. He has parted with it definitely and conclusively, 
and it forms part of the odds against which he must put 
up his money if he has to bet again to win. 


i8o 


The safe way to study the problem is to remember that 
there are three things which a man may do when it comes 
his turn to bet on his hand provided some one has already 
betted. He may either throw down his cards or call or 
raise. One of the three he must do, but either one he may 
do, according to his judgment. If he has good reason, or 
in fact any reason at all, to suppose that there is a better 
hand than his own out against it, he must either lay down 
his cards or bluff. To bet against that supposition is only 
justified in such a case as that already described, when the 
odds in the betting are more favorable than the chances of 
the cards are unfavorable, and even that is only justifiable 
when the player has the last say. 

In case it be decided to bluff, the player must calculate 
on the chances of having to encounter another bluff, and 
should be prepared to carry it out to a conclusion even if 
several more raises are necessary. If he has not sufficient 
confidence for this it is best not to attempt the bluff in the 
first place. To lay down is far better poker. 

The second proposition, to call, has already been con- 
sidered, but the third usually settles itself. It is much easier, 

‘ under ordinary circumstances, to decide when it is good 
play to raise than it is to recognize the necessity for either 
of the other alternatives. The only danger to be appre- 
hended in raising is that of overconfidence, and practice in 
playing is tolerably sure to cure that. One thing, however, 
should be remembered. The player who raises should never 
show any hesitation or doubt in doing it unless his hand is 
really so strong that he is anxious to be raised in return. 


i8i 




" Pressing the Luck." 

I T seems, at first sight, entirely incongruous to recognize 
luck as a factor to be seriously considered in a study 
of the scientific aspect of any game, even Draw Poker, 
in which hardly any one can be found to deny the exist- 
ence of luck. The obvious proposition is that, since luck 
is of its nature an uncertain thing while science should be 
certain, there can be no possibility of blending the two. 
Following this in logical sequence would seem to be the 
rule that a player who seeks to conduct his game on scien- 
tific principles must discard all considerations of luck from 
his calculations, while he who relies upon his luck need pay 
no attention to the mathematical probabilities involved in 
scientific play. 

Neither the one proposition nor the other, however, will 
be found to result in successful poker. Dispute it and ridi- 
cule it as we may, nothing is more certain than that some 
persons are more lucky than others in the matter of getting 
desirable cards in the deal and in the draw, and it is equally 
certain that every one who plays poker habitually will find 
his luck varying from time to time in this particular For 
the purpose of illustration this matter of the holding of 
cards may be considered independently of the question of 
the luck of opposing players, and the chance of any hand, 
however strong, being beaten by some other hand in the 
show-down. The inquiry will then resolve itself into the 
probability of any one player, on a given occasion, getting, 
let us say, a given card which he needs in the draw to fill 
an incomplete hand. 


182 


As simple a form as can be selected for the inquiry is 
the chance of filling a Flush. The Four Flush, lacking the 
one card needed to complete it, is a worthless hand which a 
single pair of deuces will beat, but if the fifth card of the 
suit comes in the draw, the hand at once becomes strong 
enough to justify heavy betting unless there should be plain 
indications that some other player is also exceptionally 
strong. The single-card draw to a Four Flush may there- 
fore be accepted without question as one of the things 
which exemplify the chance or luck side of the game of 
Draw Poker. At the same time it is one of the simplest 
propositions on which the scientific side of the game can 
be illustrated. 

Taking the latter side first, it may be said without the 
possibility of demur that the player drawing to a Four 
Flush has nine forty-sevenths of a certainty of filling his 
hand. That is, there are forty-seven cards in the pack 
which he has not seen after looking at the five which he 
has received in the draw, and as he holds four of some one 
suit, he knows that there are nine others of that suit among 
the forty-seven. He may reckon, therefore, with absolute 
certainty, on nine chances in forty-seven of catching the 
card he needs to make his Flush. 

Following that out in the betting, let us suppose that 
there is $38 in the pot, that it is this player’s last say, 
no one else having an opporunity to raise after he goes in, 
and that it costs him $9 to stay. If the filling of his Flush, 
then, would absolutely insure his winning the pot, it would 
be mathematically even gambling for him to put in the 
money. To proceed on this hypothesis, however, would 
be the crudest sort of play, since there remains a chance, 
and by no means a remote one, that his Flush, even if he 
secures it, may be beaten. Just what that chance is he has 
no means of figuring before the draw, excepting from the 


tables, and even that he cannot decide positively till he 
knows how high the fifth card will be of his Flush, for 
any Flush excepting a Royal may be beaten by a higher 
Flush. After the draw he may be able to form a better 
opinion as to what his opponents hold, but until he knows 
what they call for his opinion cannot be formulated. 

Practically, however, he knows that a Flush is a strong 
hand which will win more often than it will lose, and 
therefore if he can get odds of 38 to 9, or any better 
odds in the betting, it is scientifically correct play for 
him to put up his money and draw the one card. If 
he plays poker strictly according to the mathematical 
chances of the game he will follow this rule every time, 
throwing down his cards if the betting is not a trifle better 
than 4 to 1, and making the play whenever he can get those 
odds or better. Of course what he may do after the draw 
is another question which will depend not only on the card 
he draws, but on what the other players may do, and what 
he has reason to think they may hold. Each problem in 
poker, however, has to be decided as it comes up, without 
reference to what may happen afterward and solely in the 
light of what has happened before. 

It is precisely at a point like this that a man who is 
modifying his play according to his luck, or according to 
the luck of some other man at the table, will be likely to 
pause and consider how the mathematical chances of the 
game are working in actual practice. As we have seen, 
according to the tables he ought to fill his Flush nine times 
out of every forty-seven times he draws to it, and there is 
no escape from the theoretical proposition that he will do 
so. Practically it seems to depend altogether on his indi- 
vidual luck whether the table is even approximately correct. 
A record was kept by one player for over a year of his ex- 
perience in drawing to Four Flushes, and the record showed 


184 


that in the course of the year he filled his Flush only once 
out of every fourteen efforts, failing, on the average, thir- 
teen times out of every fourteen. On the other hand, the 
author has seen a player fill nine Flushes in succession 
without failing once in the nine efforts, and three times out 
of the nine he drew two cards, while once he drew three 
to an Ace and tenspot of the same suit. This was in a 
single sitting, and the game broke up before the run of luck 
was broken, so that there is no way to judge whether the 
tenth and any successive efforts would or would not have 
been successful had they been made. It has been laid down, 
however, by no less an authority than “ John Oakhurst, 
gambler,” that “ there is only one thing certain about luck, 
and that is that it is going to change.” According to this 
theory, and according to common sense as well, it would be 
manifestly foolish to expect that player, or any other, no 
matter how good his luck might be, to go on indefinitely 
filling all the Flushes he should draw to, or even a majority 
of them, in a long-continued series of efforts. 

The two instances here cited are undeniably exceptional. 
No man, however good his luck might be, would be justified 
in expecting to fill a Flush every time, and in making his 
bets on that hypothesis. He might, of course, win for a 
time, as a man might make a Royal Flush in a four-card 
draw, nothing within the range of the game being an im- 
possible occurrence, but no one excepting a maniac would 
go on risking his money on wholly improbable contingen- 
cies unless he should get wholly improbable odds in the 
betting every time, and even at that he would be likely to 
lose in the long run. 

The question is pertinent, however, and perfectly proper 
as to how far a player is justified in disregarding the math- 
ematical chances when it becomes evident that the luck is 
running strongly in his favor, or, on the other hand, when 


he is in decidedly poor luck. The answer to the question 
cannot be made in specific terms, nor would any player be 
likely to pay attention to it if it were made. Much depends, 
in a case like this, as much depends in the game of poker 
always, on the personal equation. As a matter of expe- 
rience the man of strongly sanguine temperament usually 
loses money after a run of luck, for the reason that he 
relaxes his rules of play during its continuance to such an 
extent that he fails to get the full benefit of it, and continues 
the relaxation after the luck changes so that he forfeits 
much of his winnings. 

It is entirely possible, however, for one who understands 
the principles of the game to take advantage of luck when 
it comes his way, without for a moment losing sight of the 
scientific rules which he has formulated for his own use. 
In the first place he may set it down as a certainty that 
he cannot have unusual luck for more than two or three 
hands without the other players in the game noticing it and 
taking it into their own calculations, so that they will be 
particularly cautious in playing against him until his luck 
shall turn. His first step in pressing his luck, therefore, 
may very properly be to take into account the caution or 
fear which he has inspired in his opponent, and infuse more 
of the element of bluff into his betting than is habitual with 
him. This, however, he should be careful not to overdo, 
lest, if he be called on too strong a bluff, he may dissipate 
that very belief in his luck which he reckons the others to 
have. 

The temptation in pressing the luck in this direction or 
in any other is always to overdo it. For example, in the very 
case of drawing to a Flush, which has just been considered, 
the man who is pressing his luck is likely to take odds that 
are very little in his favor, coming into a pot when he only 
gets two or three to one, and drawing to a Flush, relying 


i86 


on his luck to bring him the card that he wants and so justi- 
fying his bet. Of course, he may win. If his luck holds, 
he will, but the result is likely to be that he will still further 
relax his rules and presently lose. It is far better play for 
him to continue to keep in mind the laws of chance which 
should govern his betting before the draw, and wait until 
he finds his luck still good before plunging. It is not to 
be forgotten that though he may have filled half a dozen 
Flushes in succession, the odds against his filling the next 
one are still thirty-eight to nine, and that if he fails to fill, 
his preceding luck will be of no use to him beyond inspiring 
fear of the bluff he may decide to make. The best kind of 
luck may be frittered away by chipping against chances 
if this be done to excess, and it is much better to determine 
before playing that the luck still holds than it is to rely on 
it in the draw when the draw costs more than the math- 
ematical chances justify. 

Pressing the luck, therefore, may be set down as ex- 
tremely doubtful play beyond a narrow limit, and that limit 
it is well to fix before the draw. After the draw has deter- 
mined that there is ground for supposing that the luck is 
still good, a certain amount of confidence over and above 
what the player usually finds justified is natural, and is 
likely to prove valuable, but it is to be remembered that 
luck will bring winnings, even though the ordinary rules 
of caution be observed in the play, while nothing but the 
most extraordinary luck will pull the player through if he 
violates those rules. 

The other side of the question is as to what the player 
should do when the luck runs against him, and to this it is 
much easier to give answer. No player, however skilful 
he may be, can hope to win with the cards always against 
him, and there are therefore only two courses in a case of 
this sort. He may abandon the game for the time, or if he 


be disinclined for this, he may continue playing but refuse 
to enter any avoidable struggle unless the odds are strongly 
in his favor. In such a case he would not pay to draw cards 
to anything less than a pair of Aces, and would refuse to 
bet on those unless he bettered in the draw. And for a 
time, at least as long as he saw no signs of a change of luck, 
he would go no further than a call, even on a moderately 
strong hand. The change will come eventually, as Oak- 
hurst declares, and it is mainly a question of nerve and 
sufficient funds for a man to remain until it does change. 
Few good players, however, will continue this sort of 
struggle very long. 


Mental Discipline of the Game. 

I T is not to be disputed that the game of Draw Poker 
tends strongly toward arousing emotions which, if un- 
controlled, tend to disturb, if not destroy, the welfare 
of the individual. This fact is commonly used by those 
who condemn the game as the strongest possible argument 
against it and as a ground for denunciation, not only of the 
game itself, but of all who indulge in it. 

Those who play the game sufficiently to know it and 
who understand its principles hold different views. These 
maintain that while the game unquestionably presents op- 
portunities for the development of unworthy traits of char- 
acter, and while it does offer temptations, it is still true that 
there is no other course of training which conduces to more 
self-control or to a better mastery of the very passions in 
question than the playing of Draw Poker. That it may 
be pursued to excess or unwisely in one way or another 
is undeniable, but that is true of everything else in the en- 
tire range of human experience. The moralist who holds 
that gambling in any form is of itself sinful will listen to 
nothing in extenuation of Draw Poker, and, if logical, will 
denounce fire insurance, if not even life insurance, on the 
same grounds ; but he who recognizes that the greatest part 
of human endeavor involves something of the elements of 
gambling will be willing to admit that the game is not essen- 
tially evil and will perceive that it is extremely valuable as 
mental exercise. There is an element of moral training 
in it. 

One of the first and most important principles of the 
game is that each player's rights are absolutely conserved 


189 


and must not be infringed in the interest of any other or 
of all the other players. Even in cases in which a penalty 
is inflicted for a misplay, or an error which may be com- 
mitted purely by accident, the underlying principle is not 
that the person committing the error is to be punished. It 
is rather that no other player can be allowed to suffer by 
reason of an error for which he is not responsible. It is 
often said as explanation of this or that rule of play that 
the mistake of a player always works to his own disadvan- 
tage, and this is sometimes considered harsh. A little 
thought, however, will show that no error in poker can be 
condoned excepting at the expense of some person other 
than the one who committed the error. To inflict penalty 
for an error is therefore a guard on the rights of all, and is 
not to be considered in any other light. 

One of the rules at almost the beginning of the game 
is always considered harsh by those who have not learned 
the application of this principle. It is the one which de- 
clares a hand foul if the player picks up more than five 
cards from the board. It is not to be supposed that a player 
will lift six cards unless he is deliberately intending to cheat, 
and usually when the mistake is made it is the man who 
has made it who draws the attention of the party to the fact. 
It therefore seems harsh, undoubtedly, to see the hand 
barred out as foul while the other players go on with the 
game. The first impression of the beginner who has this 
rule enforced arainst him is that he is made to suffer for 
an entirely unintentional mistake, innocently made, and 
that the others are enforcing the rule simply because they 
are too indifferent to his interests to delay their own play 
for a moment while the cards are dealt again. 

It is only after he has learned more of the game that 
he comes to realize the importance of several truths that 
are involved. In the first place, if it be supposed that the 


190 


mistake was made by the dealer in giving six cards to some 
player instead of the regulation five, the dealer should* ac- 
cording to logic, be the one to suffer. But the dealer’s 
mistake is one that hurts nobody, and, moreover, is one 
that is liable to occur by reason of defective cards, or a lack 
of manual dexterity for which no one can be held account- 
able. In addition to that, there is no way in which the dealer 
can be punished, without punishing some one else to a 
greater extent. If the deal should be declared foul, either 
the same player would be required to deal again or the deal 
would pass to the next player. In the first case it would 
work a distinct hardship to the man who happened to have 
the best hand out in the deal already made by depriving him 
of the opportunity to play the cards that had come to him 
legitimately, and this would be really punishing the in- 
nocent. If the second alternative were adopted of passing 
the deal to the next player, it would be the age man who 
would suffer, in that he would lose the privilege of the age 
which had come to him in his turn. In neither case would 
the dealer be the sufferer, which would be the end to be 
accomplished, and as neither of those penalties would work 
justice, it would be necessary to devise some other one. 
It is difficult to see just what penalty could be fixed to suit 
the case. 

But as a matter of fact the dealer is not the real offender 
in the supposed case. Were it possible for a dealer to give 
out a foul hand to any player without that player discovering 
the fact in time to prevent being injured he would have that 
player or any other one at his mercy, and the game would 
immediately collapse, being deprived of all fairness and 
consequently of all interest. But no dealer can do this. He 
can certainly throw six cards to one player, and if the player 
lifts them from the table they become a foul hand, but be- 
cause this error of throwing the extra card is one that may 


be made without fault of the dealer and because it has no 
evil consequences necessarily, there is no penalty attached. 
No mischief whatever is done by the throwing of the extra 
card unless the player to whom it is thrown has the oppor- 
tunity to see what it is, and this opportunity he cannot have 
unless he lifts his cards. It is therefore entirely proper 
that the responsibility for the error should be fixed upon 
the man who lifts the cards. Unless he lifts them no error is 
imputed. It is perfectly easy for him to see that he has the 
proper number of cards before looking at them, and it is 
his duty as well as his privilege to make sure of this before 
looking, since he must guard his own rights if he expects 
to enjoy them. 

The real error, when this contingency arises, is thus seen 
to be committed by the man who picks up the foul hand, 
not by the man who places it before him. The entire 
responsibility rests upon him. Moreover, if there should 
be any advantage arising from the error, the man who looks 
at the extra card is the only one who can have the advan- 
tage, and it is entirely just and proper that he should be the 
one, and the only one, to suffer. 

There is a still further consideration from which it ap- 
pears that the enforcement of all penalties against the play- 
ers who make the errors, and against no one else, is really 
in the interest of each player. Since it follows that no 
player can be made to suffer by the error of another, it 
remains absolutely true that each player’s rights are 
guarded against the wrongful acts of every one at the board 
excepting himself. If all civilization could be conducted 
on an equally equitable basis, the greater part of the ills 
from which mankind now suffers would be remedied im- 
mediately. Again, it is to be observed that no penalty is 
enforced in Draw Poker beyond that of depriving a player 
of some advantage which, if he were allowed to benefit by 


it, would be tainted with unfairness and the suspicion of 
fraud. 

In other words, the element of revenge can never be 
included in any penalty. It is true that attempts have been 
made at times to enforce rules compelling a player to put 
up double the amount which he has unlawfully tried to 
win, but these attempts have failed, simply for the reason 
that no player who understands his own rights will submit 
to them. If he be shown to be in error, his claim to any- 
thing which is at stake, whether he has put up the whole of 
it or only a part, lapses instantly by reason of his error; 
but any attempt to collect a fine from what still remains in 
his possession, not having been put into the pot, or jeopard- 
ized by his own voluntary act, must fail from lack of juris- 
diction and total lack of executive power. To collect such 
a fine would partake of the nature of robbery and would be 
diametrically opposed to the principles of Draw Poker. 

One ground on which objection has sometimes been 
made to the game is that it is, as its detractors assert, a 
means by which a man seeks to deprive other men of their 
money without giving any equivalent. And this, it is as- 
serted, constitutes the essential dishonesty of gambling. A 
little consideration will prove to any fair-minded person 
that this is not true. It is, of course, true that the result 
of a game of poker is that a man either wins or loses money, 
but it is distinctly untrue to say that one player takes an- 
other’s money without giving an equivalent for it. In the 
first place, no player can take another player’s money 
directly, until after he has parted with his claim of owner- 
ship in it. When money is put into the pot by any player, 
it ceases to belong to him and becomes the common property 
of all who are still interested in it, and not until all but one 
have voluntarily reliquished all claim to it, or until all who 
are interested have agreed to submit the question of owner- 


l 93 


ship to the test of the merits of the respective hands, can 
any one person claim it. 

This may seem like splitting hairs, and undoubtedly if 
poker were a game of chance it would be idle to undertake 
to assert that the device of the pot was anything more than 
a cloak for gambling. As a matter of fact, however, poker 
is more a game of skill than it is of chance, and the struggle 
for the pot is really an effort to win by mental skill a sweep- 
stakes purse made up on perfectly equitable methods. The 
errors made by poker players, which are commonly charged 
to the game itself, are really the results of inherent faults 
of character developed under pressure, and while it may 
be admitted on the one hand that weak men succumb to the 
fascination of the game, it is also true that stronger men 
are benefited by the discipline of it. 

One of the commonest and strongest temptations of the 
game — the one which probably works more mischief than 
any other, and the one which is hardest of all to resist — 
is that which impels a man to keep on playing after he has 
lost too heavily, in the hope of recovering his losses. Prob- 
ably more money is lost under these conditions than under 
any other that arise in the game. The poker player, there- 
fore, who is really desirous of studying the game itself as 
a means of development, or as a healthful and invigorating 
mental pastime, rather than as a means of gambling, has 
no excuse if he allows himself to be drawn on into excess- 
ive and injurious indulgence, by the mere desire to recoup 
losses which he could not afford to make in the first place. 
By this weakness the gamester becomes the gambler, and 
the game itself is degraded from its proper status to the 
level of a mere gambling device. 

Excess in one man's game is moderation in another's, 
and each one must be judge of what game he can or cannot 
afford to play, and of the amount of losses he can stand 


194 


without injury. This being determined, the player who 
suffers himself to be enticed into excessive play, shows a 
weakness which of itself demonstrates the fact that he is 
not and cannot be a good poker player. It has been many 
times said that it takes a good poker player to lay down 
a strong hand, but it may also be said with equal truth that 
it takes a good poker player to quit the game when the 
proper time has come to quit. He who cannot stop when 
he should is in danger and has no right to play at all. By 
this it is not meant that a man should always stop playing 
when he has lost a certain amount, though a resolution to 
that effect (the amount to be fixed by each player for him- 
self to suit his own circumstances) would undoubtedly be 
a good one. What is meant, however, is that the player 
should always be able to see from the game itself what the 
cause of his losing is, and whether it is the part of wisdom 
for him to continue. Unfortunately, men do not, as a rule, 
pay attention to this, and comparatively few quit when they 
should. 

A continued series of losses, even of a considerable 
amount, should not always be taken as a good reason for 
quitting. But if this series of losses should really be an 
indication that the player is outclassed by his adversaries, 
it is high time for him to resign his seat unless he can 
afford to keep on losing for the sake of improving his style 
of play by studying his opponents’ methods. It is certain 
that every man must begin by playing with others who 
understand the game better than he, but it is suicidal for the 
average player to undertake to compete with experts on 
equal terms, excepting as a matter of education. It is not 
possible to arrange a handicap in the game of poker, and 
each player must acquire his knowledge and skill by com- 
petition on equal terms with all other players. It is by 
knowing whether he is outclassed that he will be enabled 
to escape serious damage. 


i95 


When a player finds himself losing steadily in a game of 
poker, he should be able to analyze the game closely enough 
to understand the reason. It may be true, and often is, that 
he is the victim of a genuine run of hard luck. It often 
happens that a player will go on for hours without holding 
any good cards at all, or if he holds any, having them out- 
classed every time by the other players’ hands. And even 
a more serious form is sometimes assumed by his bad luck, 
when he holds good hands frequently and has them beaten 
all the time by better ones. This is an element of the game 
which no man can overcome. The only possible defence 
is to play as cautiously as possible and lose as little as may 
be, till fortune smiles again and the cards begin to run the 
other way. If it were possible to foresee such runs, no man 
would play against them ; and many players, when they find 
the cards running steadily to their hurt, make it a rule to 
quit the game rather than to wait for the turn. 

Such runs of ill luck come to the best players as well 
as to others, and are by no means to be considered discour- 
aging excepting for the moment. And the fact that they 
do occur often blinds the losers to the real truth of the case, 
which may be that they are losing because they cannot play 
as well as those they are pitted against. One’s judgment 
is often blinded by a preconceived notion that he can play 
a good game, and he will blame the cards for his losses 
when he should really blame himself for not winning as 
much as he might when he holds the winning hand, and 
for losing more than he should when the others win. 

It is an essential part of good play, therefore, that a 
man should study his opponents’ game constantly from deal 
to deal, watching the winner’s play in each instance, and 
noting as closely as possible how well each man takes ad- 
vantage of his position in the betting and of the cards he 
holds. Under almost exactly similar circumstances a good 


196 


player will often make twice as much as a poor player out 
of the same hand and against similar hands held by his op- 
ponents. 

If, therefore, the loser shall see that the others at the 
board are winning more money hand by hand when they 
do win, than he himself is winning when the pots fall to 
him, he will have found one danger signal. It is true that 
this is not an infallible test. The winner in one case may 
have strong hands out against him though his own hand is 
the strongest, and in the other case the winning hand may 
have nothing opposed to it which will call for a bet, so 
that a poor player may win more on Three of a Kind in 
one deal than a good player can win on Four of a Kind 
in another. The deals are of almost infinite variety, so that 
it would be almost an impossibility to find two in which 
exactly similar hands were held all around the board, with 
each hand in the same relative position. 

The principles governing the play, however, are always 
the same, and it is possible for any good player, by watch- 
ing a game for a while, to tell which one of those engaged 
in it is playing with the most nerve and the highest skill. 
Such observation is proverbially more difficult to one who 
is playing than to one who is looking on, but the player who 
is bent on learning all he can of the game must make it a 
rule to observe all the peculiarities of every man with whom 
he is playing, studying not only his style of handling his 
cards, but also his habit of betting, and the degree of 
aptitude with which he takes advantage of his chances of 
position, and the accuracy with which he gauges or seems 
to gauge the hands he has to play against. 

If, then, the loser discovers that there are men in the 
game who win, when they do win, more than he does, when 
he wins, and if it appears that this preponderance of win- 
nings comes, not from the accidents of the game giving bet- 


i 9 7 


ter opportunities, but from the superior skill with which 
advantage has been taken of those accidents, it is high time 
to withdraw. It will be urged that this withdrawal in the 
face of superior skill requires an amount of self-control that 
few men possess, and further that the only way a man can 
learn to play a really excellent game of poker is by studying 
the game of those who play better than he does, and so 
learning how to place himself on an equality with them. 
The truth is, however, that it is precisely this quality of self- 
control which is one of the prime necessities in the personal 
make-up of a really good poker player, and as to the neces- 
sity of playing with experts in order to become an expert, 
there is room for considerable doubt. 

It is certainly true that much can be learned by playing 
against experts, but it is an expensive course of tuition, 
and the same results can probably be attained by playing 
with those who have only the same degree of skill, ap- 
proximately, with yourself, providing you study the prin- 
ciples of the game and apply them so far as you can, ex- 
perimentally, in your own play. Moreover, the man who 
has the opportunity to watch the play of experts as an on- 
looker can really, if he is a good student, learn more than 
the man of equal skill who is playing in the game. In some 
fashion, however, either as onlooker or participant, the 
student must give long and patient endeavor to the game 
before he can hope to play it as it should be played. He 
may play it successfully, without much knowledge of the 
game, if the cards happen to run his way; but he cannot 
play the game without good cards unless he studies the 

principles closely, 


The Game Now Symmetrical, and Not Likely 

to be Changed. 

T HERE have been many attempts made, and probably 
there will be many more, as time goes on, to improve 
the game of Draw Poker by introducing new hands 
and by arbitrarily changing the rules of play in this and 
that particular, but it may be said generally that such 
attempts within the last thirty years have been failures. 
It is difficult to speak with precise accuracy concerning 
the genesis of the game, since no written record of it exists 
so far as is known to the public to-day. The original 
“ Hoyle,” in which book all known games of importance 
are described, which is even yet accepted as authority on 
disputed questions, makes no mention of poker; and al- 
though later editions of “ Hoyle ” have appeared in which 
poker has been described and its rules formulated, the fact 
that this work has been done by unknown authors has de- 
prived it of all title to authority, and it remains true to-day 
that no work on the subject is unchallenged. 

All that is positively known is that poker in a crude 
form began to be played in America in the first half of the 
nineteenth century and immediately caught the fancy of the 
American people. Up to the time of the Civil War, by 
which time it had come to be known as the great American 
game of cards, one improvement after another had been 
introduced until the game was usually played almost ex- 
actly, if not exactly, as it is now. The latest feature that 
has won universal favor was not, however, played in all 
circles until after the war, though it had already become 
popular and was coming to be acknowledged as a genuine 



improvement. This was the Straight Flush, how held by 
all players to be the highest hand in the deck. The Straight 
Flush is itself a development of the Straight, which was, 
when first proposed, considered a bastard hand, concerning 
the value of which there has always been controversy. It 
was ranked lower than Three of a Kind for a considerable 
time, but was afterward fixed as the next in value below a 
Flush. There are many players, however, who are not satis- 
fied with this classification, and in some circles it is now 
considered more valuable than the Flush, while a few play- 
ers are inclined to rank it higher even than a Full. 

Without going into a discussion, at this point, of the 
higher mathematics of the game, which, properly speaking, 
afford the ultimate test of the actual value of any hand, 
it may be said that the rules of poker, in the absence of any 
recognized authority, rest on the common consent of play- 
ers, and that as this common consent can only be obtained 
as a result of practical experience in playing, it is still true 
that there are variations in these rules in different places, 
but that the tendency is for them to become more and more 
uniform. As a matter of fact they are pretty nearly uni- 
form now, the test of experience having been so generally 
applied to all the attempted improvements, that only those 
which are practically in accord with the genius of the game 
have been generally adopted. 

So far as the Straight is concerned, it is enough to say 
that as the game is usually played a Flush beats a Straight, 
but that there are circles in which the Straight beats a Full. 
It must be acknowledged that, mathematically speaking, it 
is easier to fill a Four Flush than a Four Straight, since 
there are nine chances in forty-seven filling the Flush and 
only eight in forty-seven filling a Straight. 

On what theory the Straight can be held higher than 
the Flush, however, it is difficult to understand, since the 


200 


Flush is certainly the rarer hand of the two. It is easier 
to fill a Four Flush than a Four Straight, but the Four 
Straight is the more often held. 

But, while it would be absurd to say of any such thing 
as a game, and more especially of such a complicated game 
as Draw Poker, that it cannot be improved, it is certainly 
true that the game is now so logical and so symmetrical 
in its arrangement of parts that no great change in it is 
to be anticipated. There is, of course, always room for 
improvement in any human institution, more especially in 
anything in the nature of a pastime, but the fact that Draw 
Poker has been played as much as it has, by such keen and 
intellectual gamesters, for so long a time without radical 
change may be taken as at least presumptive evidence that 
it is now practically perfect. For nearly half a century, 
roughly speaking, it was undergoing the formation process, 
and for nearly a third of a century it has been practically 
at a standstill, and this is a fair indication that no further 
changes are likely. 

In the absence of any definite information, all state- 
ments of the origin of the game must of necessity be purely 
conjectural. Even the original name, Poker, is unexplained. 
It is probable, however, that the game itself began from 
a series of bets on the turn of a card. Just how or why the 
number of cards was at first limited to five can only be 
imagined, but it is a fact that the draw was unknown for a 
considerable period, and that, after it was introduced, there 
was a time when two games were played. They were called, 
by way of distinction, Draw Poker and Poker or Straight 
Poker. At the present time, however, the earlier game is 
not played at all, the superior merit of Draw Poker being 
universally acknowledged, and the game being always 
played in the improved form. 

Another bit of evidence to the effect that poker origi- 


201 


nated, as was said, in betting on the turn of a card is to be 
found in a form of the game known as stud-horse poker. 
This was played very generally in the West thirty or forty 
years ago, and, indeed, has been said to be the oldest known 
form of poker. It has gone out of fashion so completely 
that it is actually unknown to many of the poker players 
of to-day, but a brief account of it is worth giving, not 
merely as a matter of curiosity, but as indicating the way 
in which the present game has been developed. 

In stud-horse poker, after the shuffle and cut, the dealer 
delivers to each player one card, face down. After each 
one has looked at his card he deals one more card around, 
face upward. This lies on the table exposed, and betting 
is in order. When all the bets have been made that are 
desired, a third card is dealt to each player, face up. Then 
more bets may be made. The fourth card is dealt like the 
second and third, face up, and bets may be made once more 
before the last card is given out. This last one is dealt also 
face up, and the final betting goes on till all but the winner 
has been brought to a standstill. 

As will be seen, stud-horse poker affords unlimited 
opportunity for bluffing and for heavy play, but it is crude 
and almost brutal in its fierceness, compared with the more 
subtle and intellectual play in Draw Poker. Such as it is, 
however, it is one form through which the game passed 
in its development. 

By a consideration of this development it will be seen, 
readily enough, how the various hands or combinations 
possible in five cards have come to be classified, the value of 
the cards being borrowed from the game of whist, and the 
only puzzle being as to how the Straight came to be over- 
looked in the first place, and why it was so slow, as it un- 
doubtedly was, in obtaining the recognition which was 
its due. 


202 


This much as to the classification of hands. The rules 
governing the betting are only such as insure orderly 
procedure and an equal opportunity to each player. While 
these rules certainly vary in different places, the tendency 
is toward uniformity, and as one form comes to be acknowl- 
edged better than another, it comes into the more general 
acceptance. One object of this present work is to demon- 
strate the reason of each rule and show the superiority of 
the one preferred in cases in which there has been a conflict 
of authority. 

As to other proposed changes there is only one thing to 
be said. Whenever it shall be discovered that a new hand, 
or a new valuation, is of a nature that is likely to increase 
the pleasure or the excitement of the game, it will probably 
be tried by some players of an experimental turn of mind. 
If it shall prove to be entirely in harmony with the spirit 
of the game and with the rules governing the game as it 
is played now, and if, moreover, it shall be found to be an 
enjoyable addition, the chances are that it will spread from 
one circle to another until it shall come to be talked about 
by players generally. It will then, if of sufficient apparent 
value to be considered favorably, be tried by more and 
more players, until it may possibly come to be considered 
a legitimate part of the game. Gamesters of all kinds, 
however, are notoriously conservative, and poker players 
are especially so, and the chances of any more changes be- 
ing made are therefore small. 

For example, the use of the joker as a fifty-third card, 
with a value above any other card, has been looked on by 
many players as a real improvement. There is, however, 
an incongruity apparent at the very outset in this proposi- 
tion. The value of the cards in poker, as was said, is based 
on their whist values, and there is not, and cannot be, room 
for a joker in the game of whist, it being borrowed from 


203 


the totally dissimilar game of euchre. This incongruity 
may not amount to a valid objection to the use of the joker, 
but it undoubtedly accounts for the disinclination of ex- 
perienced poker players to adopt it. The general feeling 
was well expressed by a veteran poker player two or three 
years ago, when he said: “ They asked me to join in a 
game of poker a little while ago, and I was going to do it, 
for I like poker when the stakes are not too large, but they 
told me they were playing with a joker. Now they may 
get up a game of poker one of these days with high, low, 
jack, big and little cassino and the right and left bowers in 
it, and it may prove to be a game that will be greatly en- 
joyed by those who like to play it. Certainly, I will have 
nothing to say against it. But I shall not consider the 
game as poker. When I play poker, I prefer to play the 
game I learned as poker, so I declined the invitation/' 

It would be rash, however, to say that poker will be 
generally played with a joker in the pack at some future 
day. It certainly adds to the variety of the game, for the 
lucky player who catches it in the deal can call it whatever 
he chooses, so that it not only increases the chances of fill- 
ing any hand now played, but it introduces an entirely new 
set of hands — Five of a Kind — into the game. More- 
over, there is nothing about this use of an extra card, which 
is inherently discordant with the game as it is usually 
played. It is enjoyed by many undoubtedly good players, 
and it is even declared by some that its use is increasing, 
so that, in spite of the prejudice against it, there is a pos- 
sibility that it may win out. It would be difficult, how- 
ever, to induce an orthodox player to admit the probability 
of such an outcome. 

The joker is usually classed by such players as a com- 
panion of what are called freak hands, such as are proposed 
from time to time, but which have not yet been accorded 


204 


any recognition by really good players. This classification 
is not entirely just, though it is perhaps not wholly unjust. 
Certainly none of the freak hands have yet been generally 
adopted; but it is always possible that some combination 
will be discovered, which has value and character enough 
to command respect. 

It was thought at one time that such a hand had been 
discovered in the blaze. This consisted of any five court 
cards. There was necessarily one pair in it, and sometimes 
two pairs, but its rank as a blaze was above two pairs and 
below Three of a Kind. As a hand it had an apparently 
distinctive character, since it was not readily to be mistaken 
even at a glance, and the percentage of chances against its 
being held in any given deal could easily enough be figured ; 
but even among those who at first felt disposed to accept 
it as a member of the poker family of hands, it was not 
considered satisfactory, and after a brief and partial rec- 
ognition it was rejected and soon forgotten. 

The blaze, however, though it was so little thought of, 
and so soon discarded, was a better pretence at a hand than 
the so-called alternate Straight which was seriously pro- 
posed some years ago as a hand to be recognized. This 
is nothing more nor less than the sequence which omits 
each alternate card, as the deuce, four, six, eight and ten, 
or the Ace, Queen, ten, eight and six. Fantastic as the 
notion may seem to real students of the game, arguments 
were made, by some who strove to increase the possibilities 
of poker, in favor of recognizing the alternate Straight as 
a regular hand and assigning it a rank next to the Straight 
proper. It seems almost needless to say that these argu- 
ments did not prevail. Almost the only thing that could 
be said in their favor was that it was just as easy to figure 
the percentage of the chance of holding the alternate 
Straight as of the chance of any other hand. The obvious 


205 


reply to that was that, while it was undoubtedly easy to 
figure the percentage, it would be found by such figuring* 
that the hand, which was not a satisfactory hand at best, 
would necessarily be ranked very much higher than the 
Straight if ranked at all, since there were nine possible 
Straights in every deal against every six possible alternate 
Straights, and anyhow, that the alternate Straight had a 
mongrel appearance, and not having a strongly defined, 
characteristic aspect, was unsatisfactory in every way. It 
was never adopted in any play unless as an experiment, 
and is now never referred to, excepting derisively, as a 
Chicago pelter. And, as it is utterly hopeless to attempt 
to better the Chicago pelter in the draw, it is commonly 
said that the only thing to do with it is to stand pat and 
bet all you have. As the value of such play consists en- 
tirely in the way in which the bluff is put up, the alternate 
Straight may properly be considered as having no value 
whatever. 

There is a variation of poker reported as being played 
considerably in Mississippi and in certain of the river towns 
that may be supposed to have learned the new wrinkle from 
Mississippi players. It consists of including two new hands 
in the list of those having value assigned to them. The two 
hands are called little dog and big dog. The little dog is 
a hand running from deuce to seven, with any one of the 
intermediate cards — either the trey, four, five or six — 
missing. The big dog is a similar hand running from nine 
to Ace, with either the ten, Jack, Oueen or King lacking. 
Fortunately, this particular form of mental weakness has 
not yet attacked Eastern players, and there is a strong prob- 
ability that it will speedily die out, even among the feeble- 
minded players who have undertaken to introduce so absurd 
a proposition into the game. 

Equally arbitrary and equally unjustifiable by the logic 


20 6 


of the game is the custom that was introduced twelve or 
fifteen years ago, of allowing a player to open a jack-pot 
on a pair of deuces. The deuces were the only exceptions 
made to the rule that a player must have Jacks or better in 
order to open the pot; and, excepting for the privilege of 
opening, they ranked no higher than at any other time, 
so that the man who elected to open on deuces was obliged 
to play his hand purely as a bluff unless he chanced to bet- 
ter it in the draw. Moreover, the fact that he could open 
on deuces inevitably raised the suspicion that he had pos- 
sibly done so, and tended to make his bluff all the harder. 
A few notably interesting contests occurred as a result of 
the innovation, but it was decided before long that the effect 
of it was demoralizing and that it weakened the interest 
in the game instead of strengthening it. 

The device of having a deck of sixty cards instead of 
fifty-two, in order to make the game easier to play in case 
there are more than seven at the table, can hardly be 
classed with the other attempts at improvement. The pur- 
pose is not to disturb any rules or any established values, 
but merely to save trouble in the deal by avoiding the neces- 
sity of shuffling the discard anew and dealing from it, as 
it frequently becomes necessary to do when there are more 
than seven playing. To this extent it almost appears jus- 
tifiable, but there are nevertheless objections to the eleven 
and twelve cards which are introduced between the tens 
and the Jacks in order to make up the required number. 

In the first place, the very object which it is sought to 
serve by making the pack larger is an undesirable one. The 
introduction of an eighth and a ninth player into the circle 
makes the game itself too clumsy. Seven players seem to 
be the limit beyond which the circle cannot be enlarged 
without confusion and a constant possibility of delay. 

But aside from that fact, which seems to be well estab- 


207 


lished, the introduction of eight more cards into the deck 
upsets all the calculations of chances, or, rather, since new 
calculations are easily made, it tends to confuse the ordinary 
player by changing the established relation between the 
percentage of chances in the cards and the visible odds in 
the betting. As is well understood by all players, judicious 
bets can be made only by constantly bearing in mind the 
percentages of the draw. To bet judiciously, therefore, 
in a game played with a deck of sixty cards, requires a 
knowledge of a different table of chances from the one in 
ordinary use. Practically, this difference is not very great, 
but it is sufficient to disturb the player and so to affect his 
play. 

It is not pretended that all the variations and attempts 
at improvement that have been made are included in those 
that have been described in this chapter. So far from that 
being true, it is likely that scores of others have been pro- 
posed and experimented with. It remains, however, a cor- 
rect statement that the game has not been changed in any 
material particular for many years. And more than that, 
that it is not likely to be changed in any arbitrary fashion, 
or by the addition of any feature that shall not prove to 
be entirely harmonious with the existing rules that govern 
the playing of poker to-day. 





























PAGE. 

The Ten Different Poker Hands (Illustration), .... 7 

Introduction, 9 

Description of the Game, 11 

What Draw Poker Is, 13 

How the Game Is Played, 15 

Hands, 21 

Rules of the Game, . . 25 

I. Preliminaries, 27 

II. The Deal, 30 

III. Betting Before the Draw, 32 

IV. The Draw 33 

V. Betting After the Draw, 35 

VI. The Showdown and Settlement of Bets, ... 35 

VII. Jackpots 35 

VIII. Errors 39 

Calculation of Chances, 41 

I. Relative Value of Hands, 44 

II. Probable Value of Opposing Hands, ... 52 

III. Chance of Bettering in the Draw, .... 54 

IV. The Betting Odds, 58 

V. The Known and the Unknown, 61 

Studies of Actual Play, 67 

Elementary Principles 69 

The Problem of the Draw, 75 

The Limit, 85 

Personality in Poker, 94 

Betting Before the Draw, 104 

As to Laying Down, 113 

Playing a Strong Hand, 123 

The Bluff, 134 

Punctilio of the Game, 141 

How to Play Jackpots, 147 

Caution and Courage, * . 157 

The Counter Bluff, 163 

Playing Against Odds 169 

Calling and Raising, 175 

Pressing the Luck, 181 

Mental Discipline of the Game, 188 

The Game Now Symmetrical and Not Likely to be Changed, 198 

Glossary, 209 


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